title: Linear differential equation

text: It follows that, if one represents (in a computer) holonomic functions by their defining differential equations and initial conditions, most calculus operations can be done automatically on these functions, such as derivative, indefinite and definite integral, fast computation of Taylor series (thanks of the recurrence relation on its coefficients), evaluation to a high precision with certified bound of the approximation error, limits, localization of singularities, asymptotic behavior at infinity and near singularities, proof of identities, etc.


title: White Gold (TV series)

text: White Gold is a British sitcom featuring a group of UPVC window salesmen in mid-1980s Corringham, Essex. It stars Ed Westwick as Vincent, the head of a double-glazed windows sales team, with former "Inbetweeners" cast members Joe Thomas and James Buckley. BBC Two announced that series two of the show would air on 6 March 2019. Series 1 was released internationally by Netflix on 11 August 2017.


title: White Gold (TV series)

text: The show is produced by BBC Comedy along with Fudge Park Productions, which was established in 2015 by the creators of "The Inbetweeners" – Damon Beesley and Iain Morris. Beesley created White Gold and acts as show runner and executive producer, in addition to having written eight of the 12 episodes. Joe Thomas and Chris Niel wrote two episodes each.


title: White Gold (TV series)

text: Production of series 2 was suspended in November 2017 following allegations of sexual assault against Ed Westwick. Filming recommenced in November 2018, after Westwick was stated to be legally innocent by the Los Angeles District Court.


title: Edward Kenway

text: Edward James Kenway is a fictional character in Ubisoft's "Assassin's Creed" video game franchise. He was introduced as a supporting character in "", a companion novel to the 2012 video game "Assassin's Creed III". He subsequently appeared as the protagonist of the 2013 video game "" and its novelization, "Assassin's Creed: Black Flag". In the former, he is portrayed by Welsh actor Matt Ryan through performance capture. Since "Black Flag"'s release, the character has made smaller appearances in several other works within the franchise.


title: Edward Kenway

text: Within the series' alternate historical setting, Edward is a Welsh privateer-turned-pirate who is fundamental in establishing a short-lived Pirate Republic in the Caribbean in the early 18th-century. In the process, he becomes caught in the conflict between the Assassin Brotherhood (inspired by the real-life Order of Assassins), who fight for peace and freedom, and the Templar Order (inspired by the Knights Templar military order), who desire peace through control. Initially helping both sides for personal gain, he eventually has a change of heart and formally joins the Assassins after his retirement from piracy. Later in life, he settles down in London, becoming one of the co-leaders of the local branch of the Brotherhood, until his murder by the Templars in 1735. Edward is the father of Haytham Kenway, who would go on to become a high-ranking Templar and the main antagonist of "Assassin's Creed III"; the grandfather of Ratonhnhaké꞉ton / Connor, Haytham's son with a Native American woman and the protagonist of "Assassin's Creed III"; and an ancestor of Desmond Miles, the protagonist of the modern-day portions of the first five main games in the series.


title: Edward Kenway

text: Edward has received a positive reception for his charm and characterization as a morally ambiguous protagonist and self-made man, and is considered to be one of the series' most popular characters. Various merchandise for the character, as with other of the series' protagonists, has been released.


title: Edward Kenway

text: Lead scriptwriter for "Black Flag" Darby McDevitt observed that previous series protagonists have joined the Assassin Brotherhood without much deliberation, often as part of a coming of age moment, as their personal goals are already naturally aligned with that of the organization's. For "Black Flag", the developmental team wanted to explore the Assassins' tenets, their "creed", from a new perspective. The idea of a talented and shrewd pirate, a cynical and jaded man who comes into contact with the Assassins, was mooted and proposed as the protagonist who presents this different point of view and who may not share the Assassins' worldview or adherence to a higher purpose or ideal. The whole thrust of the story then became a constant conflict within Edward over the very idea of the Creed, even as he co-opts some of the Assassins' methods and tactics for his personal gain.


title: Edward Kenway

text: McDevitt explained that "Black Flag" is at its core a story of immorality and repentance, and Edward Kenway is a married man whose strained relationship with his wife is one of the central struggles in the game. McDewitt describe Edward as a "raucous and bawdy chap" who also has a few significant close relationships with other women in the story, and that his primary motivation in "Black Flag" is to get rich and prove himself a "man of quality' to his family and betters". As for his personality, McDevitt said Edward "is a pirate who yearns for freedom much like the Assassins do, but loathes the sense of responsibility that a truly functional freedom requires" and that the narrative intends to explore "at what point would Edward realize his brand of freedom is too chaotic to function for very long.” McDevitt compared Edward to his grandson Ratonhnhaké꞉ton, better known as Connor, the protagonist of "Black Flag's" antecedent "Assassin's Creed III", and described his character arc as a counterpoint in someway.


title: Edward Kenway

text: Edward Kenway is voiced by Matt Ryan, who also portrayed the character in a motion capture studio. McDevitt admitted that the character and his back story became far more influenced by the culture of Wales than he had originally intended; the developmental team only decided to build their story around a Welsh pirate when they cast Ryan as the voice and image of the character. McDevitt originally envisioned Edward to hail from an English port town like Bristol, Portsmouth, or Manchester, but deliberately left his background blank prior to the finalization of the casting process because he wanted to draw from whichever actor was chosen. McDevitt praised Ryan for the charisma and the personality he brought to the character, but recalled that he initially read his lines in a West County accent. Ryan was then asked to speak in his natural Welsh accent, which ultimately prompted McDevitt to finalize Edward as a Welsh character from Swansea, which matches his actor's cultural background. McDevitt consulted Ryan's father for ideas as he wanted to include some colloquial Welsh phrases into the game's dialogue.


title: Edward Kenway

text: Ryan noted that unlike the majority of the game's cast of characters who are fictionalized versions of historical figures, Edward is an original character. To prepare for the role, Ryan was asked to read books recommended by McDevitt as part of their research of the time period, as the game's developmental team wanted to avoid the usual tropes and archetypes associated with the depiction of piracy in popular fiction.


title: Edward Kenway

text: As a Welshman born into a family of farmers in 1693, Edward Kenway is from a low socio-economic background. At some point in his life, he fell in love with a wealthy girl named Caroline Scott. Disobeying the wishes of her parents, Caroline left her comfortable life to marry Edward. Unsatisfied with his wages on the farm, Edward quickly became a drunkard with dreams of becoming rich as a privateer. Caroline lost faith in Edward and left him while concealing her pregnancy.


title: Edward Kenway

text: Edward left his homeland to search for his fortune, first as a privateer, then as a pirate. He was active in the West Indies from 1712 to 1722 during the later years of the Golden Age of Piracy and was known for his close relationship with the likes of Adéwalé, Blackbeard, Mary Read and Anne Bonny. He commanded the "Jackdaw", a brig he had captured from the Spanish treasure fleet in 1715, and inadvertently became involved in the Assassins' and the Templars' search for an ancient place called the Observatory, which Edward intended to use for personal gain. Although Edward's career in piracy was largely a success, helping to establish an independent Pirate Republic in Nassau, he began to reflect on his life after the Republic's collapse in 1718, as well as the deaths of many of his allies. Eventually, he decided to join the Assassin Brotherhood, who sought to preserve peace and the freedom of mankind, and helped them eliminate their Templar rivals and seal away the Observatory.


title: Edward Kenway

text: In 1722, Edward was informed of Caroline's passing two years prior and the existence of his daughter, Jennifer, and arranged to meet the latter. One year later, he retired from piracy for good and relocated to London with Jennifer, donating the "Jackdaw" to the Assassins. He used his gained wealth to buy an estate in Queen Anne's Square, and took up responsibilities as a member of the Assassin Brotherhood, eventually becoming one of the co-leaders of the British Brotherhood alongside a man named Miko. During this time, Edward met and married Tessa Stephenson-Oakley, the daughter of a wealthy landowner, and had his second child with her: Haytham Kenway. In 1735, he was murdered in his estate by agents acting under orders from Reginald Birch, one of his employees and, secretly, the Grand Master of the British Rite of Templars. Following Edward's death, Birch, taking advantage of the fact that Edward had never told his son of his true affiliations, manipulated Haytham into joining the Templars. Though Haytham learned the truth and killed Birch in revenge years later, he chose to stay a Templar.


title: Edward Kenway

text: In "Assassin's Creed IV: Black Flag", the player experiences Edward's life and exploits in the Caribbean and the west coast of the African continent as part of a simulation played by a silent protagonist who works as a research analyst at Abstergo Entertainment, a corporate front of the Templar Order in the modern era. The plot of "Black Flag" follows Edward's interactions with fictionalized versions of historical figures who were active during the Golden Age of Piracy, including Stede Bonnet, Woodes Rogers, Laureano de Torres y Ayala, Mary Read, Charles Vane, Jack Rackham, Benjamin Hornigold, Blackbeard, Anne Bonny, and Bartholomew Roberts. In the alternate version of historical events depicted in "Black Flag", Edward is personally involved with several notable incidents that occurred during the time period, including the founding of the Republic of Pirates at Nassau on New Providence island, Blackbeard's blockade of Charles Town in May 1718, the Battle of Ocracoke Inlet on November 22, 1718, and the trial of Read and Bonny at Port Royal on November 16, 1720.


title: Edward Kenway

text: After learning about a mysterious location known as the Observatory, which he erroneously believes as housing treasure that would set him up financially for life, Edward is determined to secure access at any cost. He actively avoids choosing a side permanently, and is willing to utilize opportunities from both the Templars and the Assassins to achieve his goal. He begins to have a change of heart following the death of Read, who had consistently appealed to Edward's conscience throughout their friendship, and permanently sides with the Assassins towards the end of his piracy career. In the ending of "Black Flag", he is reunited with Jennifer, a daughter he never knew he had and who would insist on using her mother's surname Scott as an adult.


title: Edward Kenway

text: Edward's first appearance in the "Assassin's Creed" franchise is in the 2012 novel "", authored by Anton Gill using his pen name Oliver Bowden, as the father of its point of view character, Haytham Kenway. The novel is presented as Haytham's journal, which recounts the events leading to Edward's eventual fate, and serves to bridge the narrative gap between "Black Flag" and "Assassin's Creed III" which stars the character's progeny. He is the central focus of "Assassin's Creed: Black Flag", the novelization of the 2013 video game, also authored by Gill.


title: Edward Kenway

text: Edward's legacy and his mansion serve as a plot point in the 2015 game "Assassin's Creed Syndicate", which is set in London during the 1860s, over a century after his death. He is also featured in "Dead Men's Gold", a story arc from the 2018 mobile spin-off game "Assassin's Creed: Rebellion", which serves as a prequel to the introduction sequence of "Black Flag". Like other series protagonists, Edward's outfit has been an unlockable cosmetic option in most subsequent releases, including the remastered version of "Assassin's Creed III" released in 2019.


title: Edward Kenway

text: The character has also been referenced by Ubisoft outside the "Assassin's Creed" series. In the 2020 game "" a statue of Edward can be found in an underground Assassin Tomb in London, as part of a non-canonical crossover event between the "Assassin's Creed" and "Watch Dogs" franchises.


title: Edward Kenway

text: In conjunction with Ubisoft, Todd McFarlane and his McFarlane Toys Design Group designed a highly detailed, hand-painted, and cold-cast resin limited-edition statue of Edward Kenway. Only one thousand pieces were created and distributed worldwide, and each statue includes a Certificate of Authenticity hand-signed by McFarlane.


title: Edward Kenway

text: Edward Kenway has been well received by video game journalists, with high placements on several "top character" ranking lists of "Assassin's Creed" series protagonists. "VideoGamer.com" ranked him among the best pirates in video games.


title: Edward Kenway

text: Matt Purslow from "IGN" described Edward as the "true secret weapon" of "Black Flag", the central element that binds the game's disparate elements and features together, and argued that it manages to avoid the pitfalls of over-reliance on MacGuffin plot devices like its predecessors due to the narrative focus on Edward’s personal journey. He found the character's privateer-turned-pirate background, a chancer looking for profit whose decision to steal the robes of a member of the Assassins sparks his growth from rebel to honorable captain, to be a "fresh perspective to the overarching narrative of the series". Andrei Dobra from "Softpedia" interpreted McDevitt's statements about Edward in an interview with "VG247" as indicative of a belief that the popularity of "Black Flag" is largely because the character is an unusual protagonist who trumps many established tropes concerning heroes in the franchise. In an article which offers an impression of "" Jordan Ramée from "GameSpot" reflected on his gameplay experience with Edward in "Black Flag" fondly, where combat sequences often involved head-on confrontation of foes and that Edward solves many of his problems as a pirate that's making the most of the tools of an Assassin. Evan Stallworth Carr from "The Daily Californian" found Edward Kenway to be "a deeply interesting character" who displays a "charismatic and outgoing personality" for his pirate persona. On the other hand, Carr opined that he does not fit well into the lore of the series, which in his view ultimately hurt the plot of "Black Flag". Stephen Totilo was of the opinion that while the subplot involving the wife he left behind paid off beautifully at its conclusion, Edward is a "forgettable lead" and his character arc is "shallow".


title: Edward Kenway

text: The ending sequence of "Black Flag" has attracted praise for its depiction of Edward's character development. Tom Phillips from "Eurogamer" found it to be a "surprisingly mature conclusion for a series all about stabbing people in the neck", as Kenway finally gives up a life of piracy to settle down with his newly-discovered daughter, and that it took the entirety of the narrative of "Black Flag" where his experiences of the deaths of all of his close friends and loved ones lead him to making a sensible decision about his life. Erik Kain from "Forbes" found the final moments of "Black Flag" to be "surprisingly beautiful", describing the finale as an "oddly sad and redemptive" contemplation of the character's loss which segues to his conversation with his daughter which is both playful and regretful in tone.


title: Edward Kenway

text: Nick Dinicola from "Pop Matters" found the narrative approach by "Black Flag" to be interesting, as its lead character does not become an official member of the Brotherhood of Assassins by the ending of the game; instead, the story explores both sides of the long-running Assassin-Templar conflict from the perspective of an indifferent protagonist, and allows players a better sense of the Assassins' code of conduct as Edward gradually becomes sympathetic to their cause and acknowledges that their creed is “the beginning of wisdom.” In his paper which examines the representation of female characters in the "Assassin’s Creed" Series published by St. Mary’s University of Minnesota, Stephen J. Fishburne described Edward Kenway as "capturing the ideal of masculinity and the self-made man to the greatest extent" amongst other male protagonists in the series, and noted that "the consequences of his irresponsibility are really only felt by those around him" because he is still considered the "hero of "Black Flag"". In a paper which analyzes the cultural depiction of piracy in video games, Eugen Pfister said the depiction of pirates as rebels but not revolutionaries in "Black Flag" is historically accurate. Pfister noted that while Edward mostly acts ethically and adheres to his own code of conduct as he tries to do the “right thing”, he becomes a “gentleman of fortune” of his own volition in the first place, and that even more importantly, he seeks no redemption for his violent actions when it comes to exploring and hunting for victims. This is reinforced by the game's mechanics, which encourages constant pillaging and raiding of merchant ships to improve the performance of Edward's flagship and offers the character "no incentive to ponder the possibility of becoming an honest man again".


title: Penrose tiling

text: A Penrose tiling is an example of an aperiodic tiling. Here, a "tiling" is a covering of the plane by non-overlapping polygons or other shapes, and "aperiodic" means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s.


title: Penrose tiling

text: There are several different variations of Penrose tilings with different tile shapes. The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two different rhombi, or two different quadrilaterals called kites and darts. The Penrose tilings are obtained by constraining the ways in which these shapes are allowed to fit together in a way that avoids periodic tiling. This may be done in several different ways, including matching rules, substitution tiling or finite subdivision rules, cut and project schemes, and coverings. Even constrained in this manner, each variation yields infinitely many different Penrose tilings.


title: Penrose tiling

text: Penrose tilings are self-similar: they may be converted to equivalent Penrose tilings with different sizes of tiles, using processes called "inflation" and "deflation". The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles. The study of these tilings has been important in the understanding of physical materials that also form quasicrystals. Penrose tilings have also been applied in architecture and decoration, as in the floor tiling shown.


title: Penrose tiling

text: Covering a flat surface ("the plane") with some pattern of geometric shapes ("tiles"), with no overlaps or gaps, is called a tiling. The most familiar tilings, such as covering a floor with squares meeting edge-to-edge, are examples of periodic tilings. If a square tiling is shifted by the width of a tile, parallel to the sides of the tile, the result is the same pattern of tiles as before the shift. A shift (formally, a translation) that preserves the tiling in this way is called a "period" of the tiling. A tiling is called periodic when it has periods that shift the tiling in two different directions.


title: Penrose tiling

text: The tiles in the square tiling have only one shape, and it is common for other tilings to have only a finite number of shapes. These shapes are called "prototiles", and a set of prototiles is said to "admit a tiling" or "tile the plane" if there is a tiling of the plane using only these shapes. That is, each tile in the tiling must be congruent to one of these prototiles.


title: Penrose tiling

text: A tiling that has no periods is "non-periodic". A set of prototiles is said to be "aperiodic" if all of its tilings are non-periodic, and in this case its tilings are also called aperiodic tilings. Penrose tilings are among the simplest known examples of aperiodic tilings of the plane by finite sets of prototiles.


title: Penrose tiling

text: The subject of aperiodic tilings received new interest in the 1960s when logician Hao Wang noted connections between decision problems and tilings. In particular, he introduced tilings by square plates with colored edges, now known as "Wang dominoes" or "tiles", and posed the ""Domino Problem"": to determine whether a given set of Wang dominoes could tile the plane with matching colors on adjacent domino edges. He observed that if this problem were undecidable, then there would have to exist an aperiodic set of Wang dominoes. At the time, this seemed implausible, so Wang conjectured no such set could exist.


title: Penrose tiling

text: Wang's student Robert Berger proved that the Domino Problem was undecidable (so Wang's conjecture was incorrect) in his 1964 thesis, and obtained an aperiodic set of 20,426 Wang dominoes. He also described a reduction to 104 such prototiles; the latter did not appear in his published monograph, but in 1968, Donald Knuth detailed a modification of Berger's set requiring only 92 dominoes.


title: Penrose tiling

text: The color matching required in a tiling by Wang dominoes can easily be achieved by modifying the edges of the tiles like jigsaw puzzle pieces so that they can fit together only as prescribed by the edge colorings. Raphael Robinson, in a 1971 paper which simplified Berger's techniques and undecidability proof, used this technique to obtain an aperiodic set of just six prototiles.


title: Penrose tiling

text: The first Penrose tiling (tiling P1 below) is an aperiodic set of six prototiles, introduced by Roger Penrose in a 1974 paper, based on pentagons rather than squares. Any attempt to tile the plane with regular pentagons necessarily leaves gaps, but Johannes Kepler showed, in his 1619 work "Harmonices Mundi", that these gaps can be filled using pentagrams (star polygons), decagons and related shapes. Kepler extended this tiling by five polygons and found no periodic patterns, and already conjectured that every extension would introduce a new feature hence creating an aperiodic tiling. Traces of these ideas can also be found in the work of Albrecht Dürer. Acknowledging inspiration from Kepler, Penrose found matching rules for these shapes, obtaining an aperiodic set. These matching rules can be imposed by decorations of the edges, as with the Wang tiles. Penrose's tiling can be viewed as a completion of Kepler's finite "Aa" pattern.


title: Penrose tiling

text: Penrose subsequently reduced the number of prototiles to two, discovering the kite and dart tiling (tiling P2 below) and the rhombus tiling (tiling P3 below). The rhombus tiling was independently discovered by Robert Ammann in 1976. Penrose and John H. Conway investigated the properties of Penrose tilings, and discovered that a substitution property explained their hierarchical nature; their findings were publicized by Martin Gardner in his January 1977 "Mathematical Games" column in "Scientific American".


title: Penrose tiling

text: In 1981, N. G. de Bruijn provided two different methods to construct Penrose tilings. De Bruijn's "multigrid method" obtains the Penrose tilings as the dual graphs of arrangements of five families of parallel lines. In his "cut and project method", Penrose tilings are obtained as two-dimensional projections from a five-dimensional cubic structure. In these approaches, the Penrose tiling is viewed as a set of points, its vertices, while the tiles are geometrical shapes obtained by connecting vertices with edges.


title: Penrose tiling

text: The three types of Penrose tiling, P1–P3, are described individually below. They have many common features: in each case, the tiles are constructed from shapes related to the pentagon (and hence to the golden ratio), but the basic tile shapes need to be supplemented by "matching rules" in order to tile aperiodically. These rules may be described using labeled vertices or edges, or patterns on the tile faces; alternatively, the edge profile can be modified (e.g. by indentations and protrusions) to obtain an aperiodic set of prototiles.


title: Penrose tiling

text: Penrose's first tiling uses pentagons and three other shapes: a five-pointed "star" (a pentagram), a "boat" (roughly 3/5 of a star) and a "diamond" (a thin rhombus). To ensure that all tilings are non-periodic, there are matching rules that specify how tiles may meet each other, and there are three different types of matching rule for the pentagonal tiles. Treating these three types as different prototiles gives a set of six prototiles overall. It is common to indicate the three different types of pentagonal tiles using three different colors, as in the figure above right.


title: Penrose tiling

text: Penrose's second tiling uses quadrilaterals called the "kite" and "dart", which may be combined to make a rhombus. However, the matching rules prohibit such a combination. Both the kite and dart are composed of two triangles, called "Robinson triangles", after 1975 notes by Robinson.


title: Penrose tiling

text: The matching rules can be described in several ways. One approach is to color the vertices (with two colors, e.g., black and white) and require that adjacent tiles have matching vertices. Another is to use a pattern of circular arcs (as shown above left in green and red) to constrain the placement of tiles: when two tiles share an edge in a tiling, the patterns must match at these edges.


title: Penrose tiling

text: These rules often force the placement of certain tiles: for example, the concave vertex of any dart is necessarily filled by two kites. The corresponding figure (center of the top row in the lower image on the left) is called an "ace" by Conway; although it looks like an enlarged kite, it does not tile in the same way. Similarly the concave vertex formed when two kites meet along a short edge is necessarily filled by two darts (bottom right). In fact, there are only seven possible ways for the tiles to meet at a vertex; two of these figures – namely, the "star" (top left) and the "sun" (top right) – have 5-fold dihedral symmetry (by rotations and reflections), while the remainder have a single axis of reflection (vertical in the image). Apart from the ace (top middle) and the sun, all of these vertex figures force the placement of additional tiles.


title: Penrose tiling

text: The third tiling uses a pair of rhombuses (often referred to as "rhombs" in this context) with equal sides but different angles. Ordinary rhombus-shaped tiles can be used to tile the plane periodically, so restrictions must be made on how tiles can be assembled: no two tiles may form a parallelogram, as this would allow a periodic tiling, but this constraint is not sufficient to force aperiodicity, as figure 1 above shows.


title: Penrose tiling

text: The matching rules distinguish sides of the tiles, and entail that tiles may be juxtaposed in certain particular ways but not in others. Two ways to describe these matching rules are shown in the image on the right. In one form, tiles must be assembled such that the curves on the faces match in color and position across an edge. In the other, tiles must be assembled such that the bumps on their edges fit together.


title: Penrose tiling

text: There are 54 cyclically ordered combinations of such angles that add up to 360 degrees at a vertex, but the rules of the tiling allow only seven of these combinations to appear (although one of these arises in two ways).


title: Penrose tiling

text: The various combinations of angles and facial curvature allow construction of arbitrarily complex tiles, such as the "Penrose chickens".


title: Penrose tiling

text: Several properties and common features of the Penrose tilings involve the golden ratio formula_1 (approximately 1.618). This is the ratio of chord lengths to side lengths in a regular pentagon, and satisfies = 1 + 1/.


title: Penrose tiling

text: Consequently, the ratio of the lengths of long sides to short sides in the (isosceles) Robinson triangles is :1. It follows that the ratio of long side lengths to short in both kite and dart tiles is also :1, as are the length ratios of sides to the short diagonal in the thin rhomb t, and of long diagonal to sides in the thick rhomb T. In both the P2 and P3 tilings, the ratio of the area of the larger Robinson triangle to the smaller one is :1, hence so are the ratios of the areas of the kite to the dart, and of the thick rhomb to the thin rhomb. (Both larger and smaller obtuse Robinson triangles can be found in the pentagon on the left: the larger triangles at the top – the halves of the thick rhomb – have linear dimensions scaled up by compared to the small shaded triangle at the base, and so the ratio of areas is :1.)


title: Penrose tiling

text: Any Penrose tiling has local pentagonal symmetry, in the sense that there are points in the tiling surrounded by a symmetric configuration of tiles: such configurations have fivefold rotational symmetry about the center point, as well as five mirror lines of reflection symmetry passing through the point, a dihedral symmetry group. This symmetry will generally preserve only a patch of tiles around the center point, but the patch can be very large: Conway and Penrose proved that whenever the colored curves on the P2 or P3 tilings close in a loop, the region within the loop has pentagonal symmetry, and furthermore, in any tiling, there are at most two such curves of each color that do not close up.


title: Penrose tiling

text: There can be at most one center point of global fivefold symmetry: if there were more than one, then rotating each about the other would yield two closer centers of fivefold symmetry, which leads to a mathematical contradiction. There are only two Penrose tilings (of each type) with global pentagonal symmetry: for the P2 tiling by kites and darts, the center point is either a "sun" or "star" vertex.


title: Penrose tiling

text: Many of the common features of Penrose tilings follow from a hierarchical pentagonal structure given by "substitution rules": this is often referred to as "inflation" and "deflation", or "composition" and "decomposition", of tilings or (collections of) tiles. The substitution rules decompose each tile into smaller tiles of the same shape as those used in the tiling (and thus allow larger tiles to be "composed" from smaller ones). This shows that the Penrose tiling has a scaling self-similarity, and so can be thought of as a fractal, using the same process as the pentaflake.


title: Penrose tiling

text: Penrose originally discovered the P1 tiling in this way, by decomposing a pentagon into six smaller pentagons (one half of a net of a dodecahedron) and five half-diamonds; he then observed that when he repeated this process the gaps between pentagons could all be filled by stars, diamonds, boats and other pentagons. By iterating this process indefinitely he obtained one of the two P1 tilings with pentagonal symmetry.


title: Penrose tiling

text: The substitution method for both P2 and P3 tilings can be described using Robinson triangles of different sizes. The Robinson triangles arising in P2 tilings (by bisecting kites and darts) are called A-tiles, while those arising in the P3 tilings (by bisecting rhombs) are called B-tiles. The smaller A-tile, denoted A, is an obtuse Robinson triangle, while the larger A-tile, A, is acute; in contrast, a smaller B-tile, denoted B, is an acute Robinson triangle, while the larger B-tile, B, is obtuse.


title: Penrose tiling

text: Concretely, if A has side lengths (1, 1, ), then A has side lengths (, , 1). B-tiles can be related to such A-tiles in two ways:


title: Penrose tiling

text: In these decompositions, there appears to be an ambiguity: Robinson triangles may be decomposed in two ways, which are mirror images of each other in the (isosceles) axis of symmetry of the triangle. In a Penrose tiling, this choice is fixed by the matching rules. Furthermore, the matching rules "also" determine how the smaller triangles in the tiling compose to give larger ones.


title: Penrose tiling

text: It follows that the P2 and P3 tilings are "mutually locally derivable": a tiling by one set of tiles can be used to generate a tiling by another. For example, a tiling by kites and darts may be subdivided into A-tiles, and these can be composed in a canonical way to form B-tiles and hence rhombs. The P2 and P3 tilings are also both mutually locally derivable with the P1 tiling (see figure 2 above).


title: Penrose tiling

text: (assuming the larger size convention for the B-tiles), which can be summarized in a "substitution matrix" equation:


title: Penrose tiling

text: so that the enlarged tile A decomposes into two A tiles and one A tiles. The matching rules force a particular substitution: the two A tiles in a A tile must form a kite, and thus a kite decomposes into two kites and a two half-darts, and a dart decomposes into a kite and two half-darts. Enlarged B-tiles decompose into B-tiles in a similar way (via A-tiles).


title: Penrose tiling

text: The number of kites and darts in the "n"th iteration of the construction is determined by the "n"th power of the substitution matrix:


title: Penrose tiling

text: where "F" is the "n"th Fibonacci number. The ratio of numbers of kites to darts in any sufficiently large P2 Penrose tiling pattern therefore approximates to the golden ratio . A similar result holds for the ratio of the number of thick rhombs to thin rhombs in the P3 Penrose tiling.


title: Penrose tiling

text: Starting with a collection of tiles from a given tiling (which might be a single tile, a tiling of the plane, or any other collection), deflation proceeds with a sequence of steps called generations. In one generation of deflation, each tile is replaced with two or more new tiles that are scaled-down versions of tiles used in the original tiling. The substitution rules guarantee that the new tiles will be arranged in accordance with the matching rules. Repeated generations of deflation produce a tiling of the original axiom shape with smaller and smaller tiles.


title: Penrose tiling

text: The above table should be used with caution. The half kite and half dart deflation are useful only in the context of deflating a larger pattern as shown in the sun and star deflations. They give incorrect results if applied to single kites and darts.


title: Penrose tiling

text: In addition, the simple subdivision rule generates holes near the edges of the tiling which are just visible in the top and bottom illustrations on the right. Additional forcing rules are useful.


title: Penrose tiling

text: Inflation and deflation yield a method for constructing kite and dart (P2) tilings, or rhombus (P3) tilings, known as "up-down generation".


title: Penrose tiling

text: The Penrose tilings, being non-periodic, have no translational symmetry – the pattern cannot be shifted to match itself over the entire plane. However, any bounded region, no matter how large, will be repeated an infinite number of times within the tiling. Therefore, no finite patch can uniquely determine a full Penrose tiling, nor even determine which position within the tiling is being shown.


title: Penrose tiling

text: This shows in particular that the number of distinct Penrose tilings (of any type) is uncountably infinite. Up-down generation yields one method to parameterize the tilings, but other methods use Ammann bars, pentagrids, or cut and project schemes.


title: Penrose tiling

text: In 1996, German mathematician Petra Gummelt demonstrated that a covering (so called to distinguish it from a non-overlapping tiling) equivalent to the Penrose tiling can be constructed using a single decagonal tile if two kinds of overlapping regions are allowed. The decagonal tile is decorated with colored patches, and the covering rule allows only those overlaps compatible with the coloring. A suitable decomposition of the decagonal tile into kites and darts transforms such a covering into a Penrose (P2) tiling. Similarly, a P3 tiling can be obtained by inscribing a thick rhomb into each decagon; the remaining space is filled by thin rhombs.


title: Penrose tiling

text: These coverings have been considered as a realistic model for the growth of quasicrystals: the overlapping decagons are 'quasi-unit cells' analogous to the unit cells from which crystals are constructed, and the matching rules maximize the density of certain atomic clusters. The aperiodic nature of the coverings can make theoretical studies of physical properties, such as electronic structure, difficult due to the absence of Bloch's theorem. However, spectra of quasicrystals can still be computed with error control.


title: Penrose tiling

text: The three variants of the Penrose tiling are mutually locally derivable. Selecting some subsets from the vertices of a P1 tiling allows to produce other non-periodic tilings. If the corners of one pentagon in P1 are labeled in succession by "1,3,5,2,4" an unambiguous tagging in all the pentagons is established, the order being either clockwise or counterclockwise.


title: Penrose tiling

text: Points with the same label define a tiling by Robinson triangles while points with the numbers 3 and 4 on them define the vertices of a Tie-and-Navette tiling.


title: Penrose tiling

text: There are also other related unequivalent tilings, such as the hexagon-boat-star and Mikulla–Roth tilings. For instance, if the matching rules for the rhombus tiling are reduced to a specific restriction on the angles permitted at each vertex, a binary tiling is obtained. Its underlying symmetry is also fivefold but it is not a quasicrystal. It can be obtained either by decorating the rhombs of the original tiling with smaller ones, or by applying substitution rules, but not by de Bruijn's cut-and-project method.


title: Penrose tiling

text: The aesthetic value of tilings has long been appreciated, and remains a source of interest in them; hence the visual appearance (rather than the formal defining properties) of Penrose tilings has attracted attention. The similarity with certain decorative patterns used in North Africa and the Middle East has been noted; the physicists Peter J. Lu and Paul Steinhardt have presented evidence that a Penrose tiling underlies examples of medieval Islamic geometric patterns, such as the girih (strapwork) tilings at the Darb-e Imam shrine in Isfahan.


title: Penrose tiling

text: Drop City artist Clark Richert used Penrose rhombs in artwork in 1970, derived by projecting the rhombic triacontahedron shadow onto a plane observing the embedded "fat" rhombi and "skinny" rhombi which tile together to produce the non-periodic tessellation. Art historian Martin Kemp has observed that Albrecht Dürer sketched similar motifs of a rhombus tiling.


title: Penrose tiling

text: In 1979, Miami University used a Penrose tiling executed in terrazzo to decorate the Bachelor Hall courtyard in their Department of Mathematics and Statistics.


title: Penrose tiling

text: In Indian Institute of Information Technology, Allahabad, since the first phase of construction in 2001, academic buildings were designed on the basis of "Penrose Geometry", styled on tessellations developed by Roger Penrose. In many places in those buildings, the floor has geometric patterns composed of Penrose tiling.


title: Penrose tiling

text: The floor of the atrium of the Bayliss Building at The University of Western Australia is tiled with Penrose tiles.


title: Penrose tiling

text: The Andrew Wiles Building, the location of the Mathematics Department at the University of Oxford as of October 2013, includes a section of Penrose tiling as the paving of its entrance.


title: Penrose tiling

text: The pedestrian part of the street Keskuskatu in central Helsinki is paved using a form of Penrose tiling. The work was finished in 2014.


title: Penrose tiling

text: San Francisco's 2018 Transbay Transit Center features perforations in its exterior's undulating white metal skin in the Penrose pattern.


title: Cigarette filter

text: A cigarette filter, also known as a filter tip, is a component of a cigarette, along with cigarette paper, capsules and adhesives. Filters were introduced in the early 1950s.


title: Cigarette filter

text: Filters may be made from plastic cellulose acetate fiber, paper or activated charcoal (either as a cavity filter or embedded into the plastic cellulose acetate fibers). Macroporous phenol-formaldehyde resins and asbestos have also been used. The plastic cellulose acetate filter and paper modify the particulate smoke phase by particle retention (filtration), and finely divided carbon modifies the gaseous phase (adsorption).


title: Cigarette filter

text: Filters are intended to reduce the harm caused by smoking by reducing harmful elements inhaled by smokers. They have been shown to reduce the risk of lung cancer. While laboratory tests show a reduction of "tar" and nicotine smoke, filters are ineffective at removing gases of low molecular weight, such as carbon monoxide. Most of these measured reductions occur only when the cigarette is smoked on a smoking machine; when smoked by a human, the compounds are delivered into the lungs regardless of whether or not a filter is used.


title: Cigarette filter

text: Most factory-made cigarettes are equipped with a filter; those who roll their own can buy them from a tobacconist.


title: Cigarette filter

text: In 1925, Hungarian inventor Boris Aivaz patented the process of making a cigarette filter from crepe paper.


title: Cigarette filter

text: From 1935, Molins Machine Co Ltd a British company began to develop a machine that made cigarettes incorporating the tipped filter. It was considered a specialty item until 1954, when manufacturers introduced the machine more broadly, following a spate of speculative announcements from doctors and researchers concerning a possible link between lung diseases and smoking. Since filtered cigarettes were considered safer, by the 1960s, they dominated the market. Production of filter cigarettes rose from 0.5 percent in 1950 to 87.7 percent by 1975.


title: Cigarette filter

text: Between the 1930s and the 1950s, most cigarettes were long. The modern cigarette market includes mainly filter cigarettes that are .


title: Cigarette filter

text: Cigarettes filters were originally made of cork and used to prevent tobacco flakes from getting on the smoker's tongue. Many are still patterned to look like cork.


title: Cigarette filter

text: Cigarette filters are usually made from plastic cellulose acetate fibre, but sometimes also from paper or activated charcoal (either as a cavity filter or embedded into the cellulose acetate).


title: Cigarette filter

text: Cellulose acetate is made by esterifying bleached cotton or wood pulp with acetic acid. Of the three cellulose hydroxy groups available for esterification, between two and three are esterified by controlling the amount of acid (degree of substitution (DS) 2.35-2.55). The ester is spun into fibers and formed into bundles called filter tow. Flavors (menthol), sweeteners, softeners (triacetin), flame retardants (sodium tungstate), breakable capsules releasing flavors on demand, and additives colouring the tobacco smoke may be added to cigarette filters. The five largest manufactures of filter tow are Hoechst-Celanese and Eastman Chemicals in the United States, Cerdia in Germany, Daicel and Mitsubishi Rayon in Japan.


title: Cigarette filter

text: Starch glues or emulsion-based adhesives are used for gluing cigarette seams. Hot-melt and emulsion-based adhesives are used for filter seams. Emulsion-based adhesives are used for bonding the filters to the cigarettes. The tip paper may be coated with polyvinyl alcohol.


title: Cigarette filter

text: The tobacco industry determined that the illusion of filtration was more important than filtration itself. It added chemicals in the filter so that its colour becomes darker when exposed to smoke (it was invented in 1953 by Claude Teague working for R. J. Reynolds Tobacco Company). The industry wanted filters to be seen as effective, for marketing reasons, despite not making cigarettes any less unhealthy.


title: Cigarette filter

text: In the 1970s epidemiologic evidence relative to tobacco-related cancers and data for coronary heart disease indicated a reduced risk among filter smokers for these diseases. Between 1970 and 1980 some studies showed a 20-50% reduction in risk of lung cancer for long-term smokers of filtered cigarettes as compared to smokers of non-filtered cigarettes (IARC, 1986) but later studies indicated a similar risk for lung cancer in smokers of filtered and non-filtered cigarettes. The risk reductions depend on different aspects such as the gender or whether a person is athletic, the study location, the age of the person, and when only studies providing both unadjusted and adjusted estimates were considered. Whether or not relative risk estimates are adjusted for cigarette consumption is not crucial to the conclusion of a clear advantage to filter cigarettes and tar reduction.


title: Cigarette filter

text: Various add-on cigarette filters ("Water Pik", "Venturi", "David Ross") are sold as stop-smoking or tar-reduction devices. The idea is that filters reduce tar and nicotine levels, permitting the smoker to be weaned away from cigarettes.


title: Cigarette filter

text: The tobacco industry has reduced tar and nicotine yields in cigarette smoke since the 1960s. This has been achieved in a variety of ways, including use of selected strains of tobacco plant, changes in agricultural and curing procedures, use of reconstituted sheets (reprocessed tobacco leaf waste), incorporation of tobacco stalks, reduction of the amount of tobacco needed to fill a cigarette by expanding it (like puffed wheat) to increase its "filling power", and by the use of filters and high-porosity wrapping papers. However, just as a drinker tends to drink a larger volume of beer than of wine or spirits, many smokers tend to inversely modify their smoking pattern according to the strength of the cigarette being smoked. In contrast to the standardized puffing of the smoking machines on which the tar and nicotine yields are based, when a smoker switches to a low-tar, low nicotine cigarette, they smoke more cigarettes, take more puffs and inhale more deeply. Conversely, when smoking a high-tar, high-nicotine cigarette there is a tendency to smoke and inhale less.


title: Cigarette filter

text: In spite of the changes in cigarette design and manufacturing over the last fifty years, the use of filters and "light" cigarettes neither decreased the nicotine intake per cigarette, nor lowered the incidence of lung cancer (NCI, 2001; IARC 83, 2004; U.S. Surgeon General, 2004). The shift over the years from higher- to lower-yield cigarettes may explain the change in the pathology of lung cancer. That is, the percentage of lung cancers that are adenocarcinomas has increased, while the percentage of squamous cell cancers has decreased. The change in tumor type is believed to reflect the higher nitrosamine delivery of lower-yield cigarettes and the increased depth or volume of inhalation of lower-yield cigarettes to compensate for lower level concentrations of nicotine in the smoke.


title: Cigarette filter

text: Cellulose acetate is non-toxic, odorless, tasteless, and weakly flammable plastic. It is resistant to weak acids and is largely stable to mineral and fatty oils as well as petroleum. Smoked (i.e., used/discarded) cigarette butts contain 5–7 mg (~ 0.08-0.11 gr) of nicotine (about 25% of the total cigarette nicotine content). Cellulose acetate is hydrophilic and retains the water-soluble smoke constituents (many of which are irritating, including acids, alkali, aldehydes, and phenols), while letting through the lipophilic aromatic compounds.


title: Cigarette filter

text: Cigarette butts are the most littered anthropogenic (man-made) waste item in the world. Approximately 5.6 trillion cigarettes are smoked every year worldwide. Of these, it is estimated that 4.5 trillion cigarette butts become litter every year. The plastic cellulose acetate in cigarette butts biodegrade gradually, passing through the stage of microplastics. The breakdown of discarded cigarette butts is highly dependent upon environmental conditions. A 2021 review article cites an experiment where 45-50% of cellulose acetate mass was fully degraded to CO after 55 days of controlled composting and another where negligible degradation took place after 12 weeks in pilot-scale compost.


title: Cigarette filter

text: During the act of smoking, plastic cellulose acetate fibers and tipping paper absorb a wide range of chemicals that are present in tobacco smoke. After cigarette butts are discarded, they can leach toxins including nicotine, arsenic, polycyclic aromatic hydrocarbons and heavy metals into the environment. Smoked cigarette butts and cigarette tobacco in butts have been shown to be toxic to water organisms such as the marine topsmelt ("Atherinops affinis") and the freshwater fathead minnow ("Pimephales promelas").


title: Cigarette filter

text: Atmospheric moisture, gastric acid, light, and enzymes hydrolyze cellulose acetate to acetic acid and cellulose. Cellulose may be further hydrolyzed to cellobiose or glucose in an acidic medium. Humans cannot digest cellulose and excrete the fibers in feces, because, unlike ruminant animals, rabbits, rodents, termites, and some bacteria and fungi, they lack cellulolytic enzymes such as cellulase.


title: Cigarette filter

text: Many governments have sanctioned stiff penalties for littering of cigarette filters; for example Washington State imposes a penalty of $1,025 for littering cigarette filters. Another option is developing better biodegradable filters. Much of this work relies heavily on the research about the secondary mechanism for photodegradation. However, making a product biodegradable means making it vulnerable to humidity and heat, which does not suit filters made for hot and humid smoke. The next option is using cigarette packs with a compartment for discarded cigarette butts, implementing monetary deposits on filters, increasing the availability of cigarette receptacles, and expanding public education. It may even be possible to ban the sale of filtered cigarettes altogether on the basis of their adverse environmental impact.


title: Cigarette filter

text: Recent research has been put into finding ways to use the filter waste in order to develop other products. One research group in South Korea have developed a one-step process that converts the cellulose acetate in discarded cigarette filters into a high-performing material that could be integrated into computers, handheld devices, electrical vehicle and wind turbines to store energy. These materials have demonstrated superior performance as compared to commercially available carbon, graphene and carbon nano tubes. Another group of researchers has proposed adding tablets of food grade acid inside the filters. Once wet enough the tablets will release acid that accelerates degradation to around two weeks instead of using cellulose triacetate and besides of cigarette smoke being quite acidic.


title: Romberg's test

text: Romberg's test, Romberg's sign, or the Romberg maneuver is a test used in an exam of neurological function for balance, and also as a test for driving under the influence of an intoxicant. The exam is based on the premise that a person requires at least two of the three following senses to maintain balance while standing: proprioception (the ability to know one's body position in space); vestibular function (the ability to know one's head position in space); and vision (which can be used to monitor and adjust for changes in body position).


title: Romberg's test

text: A patient who has a problem with proprioception can still maintain balance by using vestibular function and vision. In the Romberg test, the standing patient is asked to close their eyes. An increased loss of balance is interpreted as a positive Romberg's test.


title: Romberg's test

text: The Romberg test is a test of the body's sense of positioning (proprioception), which requires healthy functioning of the dorsal columns of the spinal cord.


title: Romberg's test

text: The Romberg test is used to investigate the cause of loss of motor coordination (ataxia). A positive Romberg test suggests that the ataxia is sensory in nature, that is, depending on loss of proprioception. If a patient is ataxic and Romberg's test is not positive, it suggests that ataxia is cerebellar in nature, that is, depending on localized cerebellar dysfunction instead.


title: Romberg's test

text: It is used as an indicator for possible alcohol or drug impaired driving and neurological decompression sickness. When used to test impaired driving, the test is performed with the subject estimating 30 seconds in their head. This is used to gauge the subject's internal clock and can be an indicator of stimulant or depressant use.


title: Romberg's test

text: Ask the subject to stand erect with feet together and eyes closed. Stand close by as a precaution in order to stop the person from falling over and hurting themselves. Watch the movement of the body in relation to a perpendicular object behind the subject (corner of the room, door, window etc.). A positive sign is noted when a swaying, sometimes irregular swaying and even toppling over occurs. The essential feature is that the patient becomes more unsteady with eyes closed.


title: Romberg's test

text: Because the examiner is trying to elicit whether the patient falls when the eyes are closed, it is advisable to stand ready to catch the falling patient. For large subjects, a strong assistant is recommended.


title: Romberg's test

text: Romberg's test is positive if the patient falls while the eyes are closed. Swaying is not a positive sign as it shows proprioceptive correction.


title: Romberg's test

text: Patients with a positive result are said to demonstrate Romberg's sign or "Rombergism". They can also be described as "Romberg's positive". The basis of this test is that balance comes from the combination of several neurological systems, namely proprioception, vestibular input, and vision. If any two of these systems are working the person should be able to demonstrate a fair degree of balance. The key to the test is that vision is taken away by asking the patient to close their eyes. This leaves only two of the three systems remaining and if there is a vestibular disorder (labyrinthine) or a sensory disorder (proprioceptive dysfunction) the patient will become much more unbalanced.


title: Romberg's test

text: Maintaining balance while standing in the stationary position relies on intact sensory pathways, sensorimotor integration centers and motor pathways.


title: Romberg's test

text: Crucially, the brain can obtain sufficient information to maintain balance if any two of the three systems are intact.


title: Romberg's test

text: Sensorimotor integration is carried out by the cerebellum and by the dorsal column-medial lemniscus tract. The motor pathway is the corticospinal (pyramidal) tract and the medial and lateral vestibular tracts.


title: Romberg's test

text: The first stage of the test (standing with the eyes open with hands on hips), demonstrates that at least two of the three sensory pathways are intact, and that sensorimotor integration and the motor pathway are functioning. The patient must stand unsupported with eyes open and hands on hips for 30 seconds. If the patient takes a step or removes a hand from the hip, the timer is stopped. The patient may make two attempts to complete the 30 seconds.


title: Romberg's test

text: Similar to the sensory organization test, the visual pathway would then be removed by closing the eyes. If the proprioceptive and vestibular pathways are intact, balance will be maintained. But if proprioception is defective, two of the sensory inputs will be absent and the patient will sway then fall. Similar to the Romberg Test, the patient must stand unsupported with eyes closed and hands on hips for 30 seconds. The patient may make two attempts to complete the 30 seconds.


title: Romberg's test

text: A variation of the Romberg Test, the Sharpened Romberg Test, consists of narrowing the patient’s base of support by placing feet in a heel to toe position. Nonetheless, test instructions do not specify which foot, preferred or non-preferred, should be placed in front of the other. The patient should be instructed to keep hands on hips for the whole 30 seconds. If the patient takes a step or removes hands from hips, the timer is stopped and the patient may attempt the test one more time.


title: Romberg's test

text: The sharpened Romberg does have an early learning effect that will plateau between the third and fourth attempts.


title: Romberg's test

text: Romberg's test is not a test of cerebellar function, as it is commonly misconstrued. Patients with severe cerebellar ataxia will generally be unable to balance even with their eyes open; therefore, the test cannot proceed beyond the first step and no patient with cerebellar ataxia can correctly be described as Romberg's positive. Rather, Romberg's test is a test of the proprioception receptors and pathways function.


title: Romberg's test

text: A positive Romberg's test which will show wide base gait in patients with back pain has been shown to be 90 percent specific for lumbar spinal stenosis.


title: Romberg's test

text: The test was named after the German neurologist Moritz Heinrich Romberg (1795–1873), who also gave his name to Parry–Romberg syndrome and Howship–Romberg sign.


title: Marie-Thérèse Walter

text: Marie-Thérèse Walter (13 July 1909 – 20 October 1977) was a French model and lover of Pablo Picasso from 1927 to about 1935 and the mother of their daughter Maya Widmaier-Picasso. Their relationship began when she was seventeen years old; he was 45 and married to his first wife, Olga Khokhlova. It ended after Picasso moved on to his next relationship, with artist Dora Maar. Walter is known as Picasso's "golden muse" and inspired numerous artworks and sculptures that he created of her during their relationship.


title: Marie-Thérèse Walter

text: Marie-Thérèse Walter was born on 13 July 1909 in Le Perreux, France. She was the illegitimate child of a French woman and a Swedish businessman.


title: Marie-Thérèse Walter

text: On 8 January 1927, Walter first met Picasso in front of the Galeries Lafayette in Paris. She was a respectable girl who lived with her mother and sisters at Maisons-Alfort, a suburb southeast of Paris. Picasso approached her and said, "You have an interesting face. I would like to do a portrait of you. I am Picasso". Walter was unfamiliar with his name but was flattered by the attention. The relationship began after Picasso invited Walter to visit his studio on 11 January 1927, which was situated on the floor above his apartment on Rue La Boétie. He studied her face and body and invited her to return the next day. The visits continued daily causing Walter to tell her mother that she had a job. She said, "He told me that I had saved his life, but I had no idea what he meant". A week after they first met, they were in a sexual relationship. At the time, Picasso was married to Olga Khokhlova, a Ukrainian ballerina, with whom he had a five-year-old son. He and Walter, then seventeen years old, began a relationship which was kept secret from his wife until 1935. Walter reinvigorated Picasso's artwork. He began to draw her portrait repeatedly, inspired by her fresh, athletic appearance, curves and oval face. Walter was very active, involved in rowing, gymnastics and cycling. Walter commented, "My life with him was always secret, calm and peaceful. We said nothing to anyone. We were happy like that, and we did not ask anything more".


title: Marie-Thérèse Walter

text: In the summer of 1928, the Picasso family stayed at Dinard, where Picasso also installed Walter at a summer camp for girls and arranged to see her in secret at his rented beach cabana. In July 1930, he bought a chateau at Boisgeloup close to Gisors, which he used as a studio for sculpture. His wife frequented the estate on weekends before returning to Paris, while his mistress spent the week with him. Walter was the unseen shadow of the family and became his model and muse for both paintings and sculptures.


title: Marie-Thérèse Walter

text: In September 1932, Walter nearly drowned after falling out of her kayak on the river Marne. This event caused her to contract a viral infection that resulted in hospitalisation and the loss of her hair. In response, Picasso painted "Rescue" on 20 November, an image of a woman being saved from drowning.


title: Marie-Thérèse Walter

text: In October 1932, Picasso's first major retrospective took place at the Galeries Georges Petit, which displayed numerous artworks depicting nude portraits of Walter, revealing the nature of his relationship with her. These portraits included "The Dream" and "Nude, Green Leaves and Bust."


title: Marie-Thérèse Walter

text: In 1934, Walter became pregnant. She informed Picasso on Christmas Eve 1934. Khokhlova had already left the family apartment on Rue La Boétie that year, but rather than moving in with Walter, Picasso rented a neighbouring house for her. When Khokhlova was informed by a friend that her husband had a longtime relationship with a woman who was expecting a child, she immediately left Picasso and moved to the South of France with their son, Paulo. Picasso and Khokhlova never divorced, although Picasso was intent on it and explored the legal possibilities, Khokhlova was "bitterly opposed to the whole thing"; instead she impounded his work until he came to terms eventually paying her a large allowance, they lived separately until her death in 1955.


title: Marie-Thérèse Walter

text: On 5 September 1935, Picasso and Walter's daughter, María de la Concepción, called "Maya", was born in Boulogne-Billancourt. Walter and Maya stayed with Picasso at Juan-les-Pins in the South of France from 25 March to 14 May 1936, and then moved to Le Tremblay-sur-Mauldre, from Versailles, in autumn 1937. Picasso visited on the weekends and some weekdays to play with his daughter. Maya also modeled for some of his paintings, including "Maya with Doll" (1938).


title: Marie-Thérèse Walter

text: By the time of Maya's birth, Picasso had already been seeing several other women including Alice Paalen and Valentine Hugo. Several months after the birth of Maya, he began a relationship with Dora Maar, a surrealist photographer and model for Picasso, in 1936. He maintained relationships with both women and combined their portraits in the 1937 artwork "Girl with a Red Beret and Pompom". Picasso installed Walter, her sister and mother at Villa Gerbier de Jonc in Royan, where he spent time with her on weekends away from Maar.


title: Marie-Thérèse Walter

text: Once, Walter and Maar met accidentally in Picasso's studio when he was painting "Guernica". Asked about this in later life, Picasso allegedly remarked that he had been quite happy with the situation and that when they demanded that he choose between them, he told them that they would have to fight it out themselves, at which point the two women began to wrestle. The art historian and friend of Picasso, John Richardson, said this story was not true and both Maar and Picasso told him it never happened. He said it is more likely that the event is imagined from the pictorial representation of Walter and Maar who appear as if in battle at opposite ends of the composition of "Guernica".


title: Marie-Thérèse Walter

text: On 4 December 1937, Picasso painted "Femme au béret et à la robe quadrillée (Marie-Thérèse Walter)", which depicts the fused portraits of Walter and Maar using the angular lines of Cubism and expresses his shifting affection from Walter to his new love, Maar. Walter's relationship with Picasso ended in 1940.


title: Marie-Thérèse Walter

text: In September 1939, when World War II was declared, Walter and Maya were in Royen and stayed there until spring 1941. They then moved back to Paris to live in an apartment on Île Saint-Louis. Walter was now aware of Picasso's relationship with Maar. Françoise Gilot later said that Maya lived with, "the fiction that her father worked a long way away".


title: Marie-Thérèse Walter

text: Picasso continued to visit Walter and Maya on Thursdays and Sundays for the next ten years. After the end of World War II, he moved to the South of France with Françoise Gilot. Walter only saw him on occasion but continued to write letters to him for a while. In 1955, when Khokhlova died, Picasso called Walter by phone and asked her to marry him, but she refused. Picasso did not see her again and Walter moved to the South of France. Upon the death of Picasso in 1973, Picasso's grandson Pablito was prevented from attending his funeral and consequently swallowed a bottle of bleach. Walter contacted the Minister of Health to arrange for a helicopter to transport him to the American Hospital in Paris. His brother-in-law, who was an art dealer took the call and Walter sold him two of Picasso's paintings to pay for his medical bills. However, Pablito did not survive. After Picasso's death, Walter found her continued life without him difficult. On 20 October 1977, four years after Picasso's death, she died by suicide at Juan-les-Pins, South of France.


title: Marie-Thérèse Walter

text: Walter has been described by art critics as Picasso's "golden muse". Picasso created numerous portraits of her, combining elements of Classicism and Surrealism. The sensuality of these portraits reflects the intensity of their love affair. The surrealist photographer, Brassaï stated, "He loved the blondeness of her hair, her luminous complexion, her sculptural body. At no other moment in his life did his paintings become so undulant, all sinuous curves, arms enveloping, hair in curls…"


title: Marie-Thérèse Walter

text: Walter was the model for at least three of the figures depicted in Picasso's 1937 painting "Guernica", which was his response to the Luftwaffe bombing of the Basque town. According to Diana Widmaier Picasso, Walter was, "forever an emblem of hope and peace for Picasso".


title: Marie-Thérèse Walter

text: "Woman with Vase", a bronze copy of a plaster sculpture of a fertility goddess that Picasso based on Walter in 1933 was placed on the artist's tomb at the Château de Vauvenargues.


title: Marie-Thérèse Walter

text: Walter is played by Susannah Harker in the 1996 film "Surviving Picasso". She is played by Poppy Delevingne in the 2018 television series "Genius", which focuses on the life and art of Pablo Picasso.


title: Attorney general

text: In most common law jurisdictions, the attorney general or attorney-general (sometimes abbreviated AG or Atty.-Gen) is the main legal advisor to the government. The plural is attorneys general.


title: Attorney general

text: In some jurisdictions, attorneys general also have executive responsibility for law enforcement, prosecutions or even responsibility for legal affairs generally. In practice, the extent to which the attorney general personally provides legal advice to the government varies between jurisdictions, and even between individual office-holders within the same jurisdiction, often depending on the level and nature of the office-holder's prior legal experience.


title: Attorney general

text: Where the attorney general has ministerial responsibility for legal affairs in general (as is the case, for example, with the United States Attorney General or the Attorney-General for Australia, and the respective attorneys general of the states in each country), the ministerial portfolio is largely equivalent to that of a Minister of Justice in some other countries.


title: Attorney general

text: The term was originally used to refer to any person who holds a general power of attorney to represent a principal in all matters. In the common law tradition, anyone who represents the state, especially in criminal prosecutions, is such an attorney. Although a government may designate some official as the permanent attorney general, anyone who came to represent the state in the same way could, in the past, be referred to as such, even if only for a particular case. Today, however, in most jurisdictions, the term is largely reserved as a title of the permanently appointed attorney general of the state, sovereign or other member of the royal family.


title: Attorney general

text: Civil law jurisdictions have similar offices, which may be variously called "public prosecutor general", "procurators", "advocates general", "public attorneys", and other titles. Many of these offices also use "attorney general" or "attorney-general" as the English translation of the title, although because of different historical provenance, the nature of such offices is usually different from that of attorneys-general in common law jurisdictions.


title: Attorney general

text: In regard to the etymology of the phrase "Attorney General", Steven Pinker writes that the earliest citation in the Oxford English Dictionary is from 1292: "Tous attorneyz general purrount lever fins et cirrographer" (All general attorneys may levy fines and make legal documents). The phrase was borrowed from Anglo-Norman French when England was ruled by Normans after the conquest of England in the 11th-century. As a variety of French, which was spoken in the law courts, schools, universities and in sections of the gentry and the bourgeoisie, the term relating to government got introduced into English. The phrase "attorney general" is composed of a noun followed by the postpositive adjective "general" and as other French compounds its plural form also appears as ""attorneys generals"". As compared to "major generals," a term that also originates from French ("") and also has a postpositive adjective, it also appears incorrectly as ""attorney generals"". While Steven Pinker writes: "So if you are ever challenged for saying "attorney-generals," "mother-in-laws", "passerbys" ... you can reply, 'They are the very model of the modern "major general"'" (a reference to the Major-General's Song, from the operetta "The Pirates of Penzance"). The modern title of major general is a military rank in which the word "general" is not used as an adjective but as a noun, which can be pluralized.


title: Attorney general

text: In modern public discourse, attorneys general are often referred to or addressed as “general”. In this construction, the word “general” is an adjective, and its use as a noun is incorrect. Attorneys general are not military officers, have no rank, and therefor should not be referred to as “general”.


title: Attorney general

text: Attorneys-General in common law jurisdictions, and jurisdictions with a legal system which is partially derived from the common law tradition, share a common provenance.


title: Attorney general

text: In Australia, the attorney-general is the chief law officer of the Crown and a member of the Cabinet. The Attorney-General is the minister responsible for legal affairs, national and public security, and the Australian Security Intelligence Organisation. Mark Dreyfus is the current Attorney-General. The Australian states each have separate attorneys-general, who are state ministers with similar responsibilities to the federal minister with respect to state law.


title: Attorney general

text: Functions of the state and federal attorneys-general include the administration of the selection of persons for nomination to judicial posts, and authorizing prosecutions. In normal circumstances, the prosecutorial powers of the attorney-general are exercised by the Director of Public Prosecutions and staff; however, the attorney-general maintains formal control, including the power to initiate and terminate public prosecutions and take over private prosecutions. Statutory criminal law provides that prosecutions for certain offences require the individual consent of the attorney-general. This is generally for offences whose illegality is of a somewhat controversial nature or where there is perceived to be a significant risk that prosecutions of a political nature may be embarked upon. The Attorney-General also generally has the power to issue certificates legally conclusive of certain facts (e.g., that the revelation of certain matters in court proceedings might constitute a risk to national security); the facts stated in such certificates must be accepted by the courts and cannot legally be disputed by any parties. The Attorney-General also has the power to issue a "nolle prosequi" with respect to a case, which authoritatively determines that the state (in whose name prosecutions are brought) does not wish to prosecute the case, so preventing any person from doing so.


title: Attorney general

text: The Attorney General of Canada () is a separate title held by the Canadian Minister of Justice (""), a member of the Cabinet. The Minister of Justice is concerned with questions of policy and their relationship to the justice system. In their role as attorney general, they are the chief law officer of the Crown.


title: Attorney general

text: A separate cabinet position, the Minister of Public Safety (), formerly the "Solicitor General", administers the law enforcement agencies (police, prisons, and security) of the federal government.


title: Attorney general

text: In Fiji, the role of the attorney general is defined as "providing essential legal expertise and support to the Government". More specific functions include "legislative drafting", "legal aid", "the prerogative of mercy" (advising the President), "liquor licensing" and "film censorship".


title: Attorney general

text: The current Attorney General is Aiyaz Sayed-Khaiyum. In January 2008, he sparked controversy by accepting other government positions in addition to his role as attorney general. Sayed-Khaiyum is currently responsible also for "Public Enterprise, Electoral Reform and Anti-Corruption". An article in the "Fiji Times" pointed out that "never before in the history of this nation has the Attorney-General held a portfolio dealing with matters other than the law and the judiciary", and criticised the decision.


title: Attorney general

text: The Secretary for Justice, known as the attorney-general before the Transfer of the Sovereignty in 1997, is the legal adviser to the Hong Kong Government and heads the Department of Justice. They are assisted by five law officers, namely:


title: Attorney general

text: The Secretary of Justice, appointed by the Chinese government on the advice of the Chief Executive of Hong Kong, is an "ex officio" member of the Executive Council of Hong Kong. The position is normally held by a legal professional, and was, before July 2002, a civil service position.


title: Attorney general

text: The Attorney General for India is the Indian government's chief legal advisor, and is its principal Advocate before the Supreme Court of India. They are appointed by the President of India on the advice of the Union Cabinet under Article 76(1) of the Constitution and hold office during the pleasure of the President. The current Attorney General for India is K.K. Venugopal.


title: Attorney general

text: The Attorney General of Ireland is the legal adviser to the Government and is therefore the chief law officer of the State. The Office of the Attorney General, is made up of a number of different offices:


title: Attorney general

text: Since the enactment of the Prosecution of Offenses Act 1974 the responsibility for the prosecution of indictable criminal offences is mostly in the hands of the Director of Public Prosecutions who is by law independent of the attorney general and the State. The current attorney general is Paul Gallagher, SC.


title: Attorney general

text: In the Isle of Man, the Attorney General is a Crown appointment (appointed by the UK government) and sits in the Legislative Council of the Isle of Man, 'ex officio'.


title: Attorney general

text: The Attorney General of Israel is the head of the public prosecution from the state, the person who advises the government in legal matters, the person who represents the state's authorities in the courts, and advises in preparation of law memoranda of the government in general and the Justice Minister in particular (likewise he examines and advises for private proposals for a law of Knesset members).


title: Attorney general

text: In Kenya the Attorney General is the Principal Legal Adviser to the Government and "ex officio" Member of Parliament and Cabinet. His duties include the formulation of legal policy and ensuring proper administration of Kenya's legal system including professional legal education. Assisting the attorney general in the performance of his duties as principal legal adviser to the government are:


title: Attorney general

text: The Hon. Justice (Rtd) Paul Kihara Kariuki is the current Attorney-General of Kenya as of April 2018.


title: Attorney general

text: In Kiribati, the attorney general is defined by section 42 of the Constitution as "the principal legal adviser to the Government". The Constitution specifies: "No person shall be qualified to hold or to act in the office of Attorney-General unless he is qualified to practise in Kiribati as an advocate in the High Court." The current Attorney General, as of 2016, was the Honourable Tetiro Semilota, until her nomination as Acting Chief Justice in October 2022.


title: Attorney general

text: In Malaysia the attorney-general or "Peguam Negara" (as he is referred to in Bahasa Melayu) is the principal legal adviser to the Government. He is also the principal public prosecutor in the country, and is also known as the Public Prosecutor. He has the power, exercisable at his discretion, to institute, conduct or discontinue any proceedings for an offence, other than proceedings before a Syariah court, a native court or a court-martial. The current Attorney-General of Malaysia is Idris Harun since 2020.


title: Attorney general

text: In Mauritius, the attorney-general, who should be a barrister, is the principal legal adviser to the government and holds the office of a minister.


title: Attorney general

text: The Attorney-General's Office is also responsible for the drafting of legislation, and vetting of all contracts or agreements of which the government is a party, including international agreements, treaties or conventions.


title: Attorney general

text: In Nepal, the attorney general is the chief legal adviser of the Government of Nepal as well as its chief public prosecutor. An Attorney General is appointed by the President on recommendation of the Prime Minister.


title: Attorney general

text: The Attorney General's Office is a constitutional body under the Constitution of Nepal (2015). For a person to be eligible for the post of Attorney General, they must also be qualified to be appointed as a judge of the Supreme Court.


title: Attorney general

text: In New Zealand, the attorney-general is the chief law officer and primary legal advisor of the New Zealand government. The Attorney-General is the Minister responsible for the Crown Law Office, the Parliamentary Counsel Office, and the Serious Fraud Office. Historically, the post could be held either by a politician or by a senior jurist, but today, it is invariably held by a member of Parliament. The Attorney-General attends Cabinet, but the post is not the same as the Minister of Justice. By tradition, persons appointed to the position of Attorney-General have been lawyers. Only two former attorneys-general have not been lawyers, most recently Dr Michael Cullen who held the post in 2005, and again from 2006.


title: Attorney general

text: The Attorney-General of Pakistan is the legal adviser to the government of the Pakistan and its public prosecutor.


title: Attorney general

text: The Attorney General of the Philippines was an office that existed from 1901 until 1932, when the office was abolished and its functions taken over by the Secretary of Justice. Since then, the Solicitor General of the Philippines, previously the second law officer, has been the principal law officer and legal defender of the Philippine Government. The Office of the Solicitor General is the law firm of the Republic of the Philippines. It is tasked with representing the Philippines, the Philippine Government, and all its officials in any litigation or matter requiring the services of a lawyer especially before appellate courts. It is an independent and autonomous office attached to the Department of Justice for budgetary purposes.


title: Attorney general

text: In Samoa, the attorney general is the legal adviser to the government. Since 2016, the attorney general is Lemalu Hermann Retzlaff (whose father Misa Telefoni Retzlaff also served as attorney general from 1986 to 1988)


title: Attorney general

text: The Attorney-General of Singapore is the legal adviser to the government of the Republic of Singapore and its public prosecutor. The current Attorney-General is Lucien Wong.


title: Attorney general

text: The attorney-general of Sri Lanka is the chief legal adviser of the Government of Sri Lanka and head of the attorney-general department which is the public prosecutor.


title: Attorney general

text: The office of Attorney General was established in Tonga in 1988, and was held jointly with the portfolio of Justice Minister until the two were separated in 2009. The Attorney General is defined as the "Chief Legal Advisor to Government".


title: Attorney general

text: According to the Constitution of Trinidad and Tobago, the supreme law of the nation, The Attorney General shall be responsible for the administration of legal affairs in Trinidad and Tobago and legal proceedings for and against the State shall be taken—


title: Attorney general

text: The attorney general for England and Wales is similarly the chief law officer of the Crown in England and Wales, and advises and represents the Crown and government departments in court. In practice, the Treasury Solicitor (who also has the title of Procurator General) normally provides the lawyers or briefs Treasury Counsel to appear in court, although the attorney general may appear in person. The person appointed to this role provides legal advice to the Government, acts as the representative of the public interest and resolves issues between government departments.


title: Attorney general

text: The attorney general has supervisory powers over the prosecution of criminal offences, but is not personally involved with prosecutions; however, some prosecutions (e.g. riot) cannot be commenced without their consent, and they have the power to halt prosecutions generally. Criminal prosecutions are the responsibility of the Crown Prosecution Service, headed by the Director of Public Prosecutions. The Attorney General may appeal cases to the higher courts where, although the particular case is settled, there may be a point of law of public importance at issue.


title: Attorney general

text: Under the Government of Wales Act 2006, the Counsel General is the chief legal adviser to the Welsh Government.


title: Attorney general

text: Since the prorogation of the Parliament of Northern Ireland in 1972, the Attorney General for England and Wales was also Attorney General for Northern Ireland. The separate office of Attorney General for Northern Ireland was re-created alongside the new office of Advocate General for Northern Ireland upon the devolution of policing and justice powers to the Northern Ireland Assembly in 2010.


title: Attorney general

text: Historically, the Lord Advocate was the equivalent for Scotland of the attorney general for England and Wales, being a legal advisor to the King of Scotland. After the Acts of Union 1707, the Lord Advocate became the chief legal advisor to the British government in respect of Scotland.


title: Attorney general

text: Under constitutional reforms enacted in 1999, the Lord Advocate has become an officer of the Scottish Government, while the United Kingdom Government is advised on Scots law by the Advocate General for Scotland, a position created in 1999.


title: Attorney general

text: The Lord Advocate is assisted by the Solicitor General for Scotland. The Advocate General is assisted by the Solicitor to the Advocate General for Scotland, based in Edinburgh.


title: Attorney general

text: The Attorney General of the Duchy of Cornwall is the chief legal adviser to the Prince of Wales, and there is a separate Attorney General for the Duchy of Lancaster, an appointment that is held by the Crown.


title: Attorney general

text: In the federal government of the United States, the Attorney General is a member of the Cabinet and, as head of the Department of Justice, is the top law enforcement officer and lawyer for the government. The Attorney General may need to be distinguished from the Solicitor General, a high Justice Department official with the responsibility of representing the government before the Supreme Court. In cases of exceptional importance, however, the attorney general may choose personally to represent the government to the Supreme Court.


title: Attorney general

text: The individual U.S. states and territories, as well as the federal district of Washington, D.C. also have attorneys general with similar responsibilities. The majority of state attorneys general are chosen by popular election, as opposed to the U.S. Attorney General, who is a presidential appointee confirmed by the Senate.


title: Attorney general

text: In nearly all United States jurisdictions the attorney general is the chief law enforcement officer of that jurisdiction, and as such attorney general may also be considered a police rank. The proper form of addressing a person holding the office is addressed Mister or Madam Attorney General, or just as Attorney General. The plural is "Attorneys General" or "Attorneys-General".


title: Attorney general

text: The Attorney General is the chief legal advisor of the government of Zimbabwe. The office falls under the Ministry of Justice and Legal Affairs.


title: Attorney general

text: Non-common law jurisdictions usually have one or more offices which are similar to attorneys-general in common law jurisdictions, some of which use "attorney-general" as the English translation of their titles.


title: Attorney general

text: The state attorney () represents the state in civil lawsuits. The state attorney is appointed by the Prime Minister for a period of 5 years and must have the same qualifications required to serve as a Supreme Court justice. The state prosecutor () represents the state in criminal trials and is appointed by the Minister of Justice for an indefinite period. The Minister of Justice oversees the judiciary, prosecution, policing, prison system et al.


title: Attorney general

text: The first type of attorney-general ("advocaat-generaal" in Dutch) is the public prosecutor in criminal cases at appellate courts.


title: Attorney general

text: The second type of attorney-general ("procureur-generaal", while their replacements are called "advocaat-generaal") is an independent advisor to the Supreme Court. These people give an opinion on cases (called "conclusies") in any field of law (not just criminal law), supported by a scientific staff. The Supreme Court may either follow or reject the opinion of the attorney-general (which is published together with the eventual decision). In a way, an attorney-general acts as yet another judge, but in the Dutch system that does not allow dissenting opinions to be published, it is the only way to reflect different perceptions on a case. The Procureur-Generaal also prosecutes members of parliament in the case of misfeance.


title: Bananas in Pyjamas

text: Bananas in Pyjamas is an Australian children's television series that first aired on 20 July 1992 on ABC. It has since been syndicated in many countries and dubbed into other languages. In the United States, the "Pyjamas" in the title was modified to reflect the American spelling "pajamas". It aired in syndication from 1995 to 1997 as a half-hour series, then became a 15-minute show paired with a short-lived 15-minute series "The Crayon Box", under a 30-minute block produced by Sachs Family Entertainment titled "Bananas in Pajamas & The Crayon Box". Additionally, the characters and a scene from the show were featured in the "Kids for Character" sequel titled "Kids for Character: Choices Count". The pilot episode was "Pink Mug".


title: Bananas in Pyjamas

text: The concept was inspired by the success of the song "Bananas in Pyjamas", written by Carey Blyton in 1967, on "Play School". This song, which had become a regular item on "Play School", became the theme of the new series. The series was revamped in May 2011 as a CGI animated series created by Southern Star Entertainment.


title: Bananas in Pyjamas

text: The main characters are two anthropomorphic bananas named B1 and B2. Other characters include the three teddy bears Amy, Lulu and Morgan, and Rat in a Hat. The bananas, the teddies and Rat in a Hat all live in the same neighbourhood, a cul-de-sac called "Cuddles Avenue". The bananas live next to the beach and serve as beach patrol. The teddies live next to and look after the park. Rat in a Hat works and lives at the community store. The characters enjoy eating "munchy honeycakes" and "yellow jelly".


title: Bananas in Pyjamas

text: The characters were inspired by a 1969 song written for children by British composer Carey Blyton (nephew of renowned children's author Enid Blyton). The jaunty song describes (an unspecified number of) bananas in pyjamas chasing teddy bears, with a slight twist at the end where a musical sting emphasises that the bananas like to "catch them unawares". The song was shown on the Australian version of "Play School" for many years accompanied by an animation depicting pairs of bananas in blue-and-white striped pyjamas. This led to a "banana" plush toy being created as part of the "toy cast", which formed the basis of the physical appearance of B1 and B2.


title: Bananas in Pyjamas

text: Creator, producer and showrunner Helena Harris devised the content of the ABC program at ABC Studios. Two of the bear characters, Amy and Morgan, are named after Helena Harris' children. The show was performed using human actors in elaborate costumes, in the style of the British "Tweenies" and "Teletubbies". In the show's early days, the voices of the bananas were provided by the same actors as were inside the costume, but the original actors eventually gave up that aspect of the show and substitutes wore the hot, stuffy costumes. The show aired new episodes from its 1992 debut to its eventual run in syndication in 2002. The show aired approximately three hundred episodes as well as four specials. Its debut in the United States was in 1995. It made videos and other media from 1995 to 1999. A toy line, developed by TOMY, debuted in 1996.


title: Bananas in Pyjamas

text: On 2 May 2011, a new version of "Bananas in Pyjamas", produced by Southern Star Entertainment in full CGI, was premiered on ABC2 in Australia; it was shown in other countries soon after that date. It contains new songs, stories, and characters, including Topsy the cheeky kangaroo, Charlie the inventive monkey and Bernard the wise old dog. Development of the new series commenced in 2009, and production started in early 2010. The new series contains 104 12-minute episodes.


title: Bananas in Pyjamas

text: The "Bananas in Pyjamas" were featured among other famous Australians during the parade of the 2000 Summer Olympics closing ceremony.


title: Bananas in Pyjamas

text: In 2017, the Royal Australian Mint produced a commemorative set containing five-cent and 20-cent coins to mark the 25th anniversary of "Bananas in Pyjamas". The five-cent coin, which is coloured for the first time, depicts Rat-in-a-Hat, while the twenty-cent coin depicts B1 and B2.


title: Ecological succession

text: Ecological succession is the process of change in the species structure of an ecological community over time. The time scale can be decades (for example, after a wildfire) or more or less.


title: Ecological succession

text: The community begins with relatively few pioneering plants and animals and develops through increasing complexity until it becomes stable or self-perpetuating as a climax community. The "engine" of succession, the cause of ecosystem change, is the impact of established organisms upon their own environments. A consequence of living is the sometimes subtle and sometimes overt alteration of one's own environment.


title: Ecological succession

text: Succession is a process by which an ecological community undergoes more or less orderly and predictable changes following a disturbance or the initial colonization of a new habitat. Succession may be initiated either by formation of new, unoccupied habitat, such as from a lava flow or a severe landslide, or by some form of disturbance of a community, such as from a fire, severe windthrow, or logging. Succession that begins in new habitats, uninfluenced by pre-existing communities is called primary succession, whereas succession that follows disruption of a pre-existing community is called secondary succession.


title: Ecological succession

text: Succession was among the first theories advanced in ecology. Ecological succession was first documented in the Indiana Dunes of Northwest Indiana and remains an important ecological topic of study.


title: Ecological succession

text: Precursors of the idea of ecological succession go back to the beginning of the 19th century. As early as 1742 French naturalist Buffon noted that poplars precede oaks and beeches in the natural evolution of a forest. Buffon was later forced by the theological committee at the University of Paris to recant many of his ideas because they contradicted the biblical narrative of Creation.


title: Ecological succession

text: Swiss geologist Jean-André Deluc and the later French naturalist Adolphe Dureau de la Malle were the first to make use of the word "succession" concerning the vegetation development after forest clear-cutting. In 1859 Henry David Thoreau wrote an address called "The Succession of Forest Trees" in which he described succession in an oak-pine forest. "It has long been known to observers that squirrels bury nuts in the ground, but I am not aware that any one has thus accounted for the regular succession of forests." The Austrian botanist Anton Kerner published a study about the succession of plants in the Danube river basin in 1863.


title: Ecological succession

text: Ragnar Hult's 1885 study on the stages of forest development in Blekinge noted that grassland becomes heath before the heath develops into forest. Birch dominated the early stages of forest development, then pine (on dry soil) and spruce (on wet soil). If the birch is replaced by oak it eventually develops to beechwood. Swamps proceed from moss to sedges to moor vegetation followed by birch and finally spruce.


title: Ecological succession

text: Between 1899-1910, Henry Chandler Cowles, at the University of Chicago, developed a more formal concept of succession. Inspired by studies of Danish dunes by Eugen Warming, Cowles studied vegetation development on sand dunes on the shores of Lake Michigan (the Indiana Dunes). He recognized that vegetation on dunes of different ages might be interpreted as different stages of a general trend of vegetation development on dunes (an approach to the study of vegetation change later termed space-for-time substitution, or chronosequence studies). He first published this work as a paper in the "Botanical Gazette" in 1899 ("The ecological relations of the vegetation of the sand dunes of Lake Michigan"). In this classic publication and subsequent papers, he formulated the idea of primary succession and the notion of a sere—a repeatable sequence of community changes specific to particular environmental circumstances.


title: Ecological succession

text: From about 1900 to 1960, however, understanding of succession was dominated by the theories of Frederic Clements, a contemporary of Cowles, who held that seres were highly predictable and deterministic and converged on a climatically determined stable climax community regardless of starting conditions. Clements explicitly analogized the successional development of ecological communities with ontogenetic development of individual organisms, and his model is often referred to as the pseudo-organismic theory of community ecology. Clements and his followers developed a complex taxonomy of communities and successional pathways.