patterns nature patterns nature visible form found natural world patterns different contexts modelled natural patterns include trees waves cracks stripes early greek philosophers studied pattern attempting explain order nature modern understanding visible patterns developed gradually time 19th century belgian physicist examined soap films leading concept minimal surface german biologist artist painted hundreds marine organisms emphasise symmetry scottish biologist thompson pioneered study growth patterns plants animals showing simple explain spiral growth 20th century british mathematician predicted mechanisms rise patterns spots stripes hungarian biologist french american mathematician showed mathematics create plant growth patterns mathematics physics chemistry explain patterns nature different levels patterns living things explained biological processes natural selection sexual selection studies pattern formation use computer models simulate wide range patterns history early greek philosophers attempted explain order nature anticipating modern concepts looking work natural patterns argued existence considered consist ideal forms form physical objects imperfect copies flower roughly circular perfect mathematical circle explained patterns nature like harmonies music arising number took basic constituent existence extent anticipated darwin evolutionary explanation structures organisms introduced number sequence western world book gave unrealistic biological example growth numbers theoretical rabbit population thompson published book growth form description sequence mathematical relationships spiral growth patterns plants classic showed simple describe apparently complex spiral growth patterns animal horns shells belgian physicist formulated mathematical problem existence minimal surface given boundary named studied soap films plateau laws describe structures formed films german psychologist claimed golden ratio expressed arrangement plant parts skeletons animals branching patterns veins nerves geometry crystals painted beautiful illustrations marine organisms particular symmetry support faux theories evolution american photographer took better known work computing wrote analysis mechanisms needed create patterns living organisms process called predicted chemical reactions particular reaction mechanisms suggested generate patterns stripes spots animals contribute spiral patterns seen plant hungarian theoretical biologist developed system formal grammar model plant growth patterns style systems alphabet symbols combined production rules build larger strings symbols mechanism translating generated strings geometric structures centuries slow development mathematics patterns wrote famous paper long coast britain mathematical thought concept causes living things like tail abstract designs beauty form pattern colour artists struggle match beauty people perceive nature causes different levels notably mathematics patterns physically form living things effects natural selection govern patterns evolve mathematics seeks discover explain abstract patterns kinds visual patterns nature find explanations chaos theory mathematical patterns example systems form convincing models different patterns tree growth laws physics apply mathematics real world perfect example crystal perfect structural defects fully exact mathematical perfection approximate real objects visible patterns nature governed physical laws example explained fluid dynamics biology natural selection cause development patterns living things reasons including camouflage sexual selection different kinds signalling including cleaning plants shapes colours patterns flowers like lily evolved insect plants wind birds bats european honey bees insects attracted flowers radial pattern colours stripes visible light serve guides seen distance scent rewards sugar rich edible types pattern symmetry symmetry living things animals mainly mirror symmetry leaves plants flowers plants radial symmetry flowers groups animals sea symmetry found group includes sea sea non living things striking symmetry unique structure forming record varying conditions nearly pattern growth arms crystals general variety crystal habits cubic true crystals symmetry unlike symmetry found different scales non living things including crown shaped splash pattern formed drop falls pond shape rings planet like saturn symmetry variety causes radial symmetry suits organisms like sea adults food threats arrive direction animals direction necessarily upper lower sides head tail ends left right head specialised mouth sense organs body internal organs need reason symmetry early symmetrical larvae argue loss old symmetry developmental ecological causes trees infinitely self similar mathematical having dimension infinite iteration possible nature patterns approximate example leaves self similar levels like growth patterns occur plants animals including like air non living things notably electrical system model different patterns tree growth varying small number parameters including branching angle distance branch points length number branches branch point like patterns occur widely nature phenomena diverse clouds river networks fault lines mountains coastlines animal coloration snow crystals blood vessel branching ocean waves common plants animals notably example chamber shell approximate copy scaled constant factor arranged spiral given modern understanding growth spiral seen special case self similarity plant seen arrangement leaves stem arrangement parts composite flower heads seed heads like fruit structures like snake fruit pattern scales pine multiple run clockwise arrangements explanations different levels mathematics physics chemistry biology individually correct necessary generated sequence runs subsequent number sum preceding ones example leaves alternate stem rotation spiral touches leaves pattern ratio ratio pear disc arranged spiral numbering mature elements size approximate golden angle spiral point view physics lowest energy configurations emerge spontaneously self organizing processes dynamic systems point view chemistry spiral generated reaction process involving activation controlled proteins manipulate concentration plant growth alongside mechanisms control relative angle stem biological perspective arranging leaves far apart possible given space favoured natural selection access resources especially sunlight chaos flow mathematics system chaotic highly sensitive initial conditions called butterfly effect requires mathematical properties mixing dense periodic alongside chaos theory ranks essentially universal influence patterns nature relationship chaos strange chaotic systems dimension cellular simple sets mathematical rules generate patterns chaotic behaviour notably rule vortex streets patterns created separation flow fluid air water objects smooth flow starts break size velocity flow large compared fluid bends rivers channels form fluid water flows bends soon path slightly curved size loop increases flow material like sand gravel river inside bend outside loop left clean unprotected erosion increasing powerful positive feedback loop waves dunes waves disturbances carry energy mechanical waves medium air water making pass wind waves sea surface waves create characteristic chaotic pattern large body water statistical behaviour predicted wind wave models waves water wind pass sand create patterns winds blow large bodies sand create dunes extensive fields desert dunes form range patterns including long straight lines stars longitudinal sword shapes crescent dunes produced wind acting desert sand horns crescent slip face point sand blows face stands degrees horizontal falls slip face angle sand degrees slip face exceeds angle sand behaviour addition small amounts sand causes happen addition small suddenly causes large apart behave like solitary waves bubbles foam soap bubble forms sphere surface minimal area smallest possible surface area volume enclosed bubbles form complex shape outer surfaces bubbles spherical surfaces joined spherical surface smaller bubble slightly larger foam mass bubbles different materials occur nature composed soap films obey plateau laws require soap films meet edge soap edges meet angle plateau laws require films smooth continuous constant average point example film remain nearly flat average curved direction left right curved downwards direction structures minimal surfaces tents lord identified problem efficient way pack cells equal volume foam solution uses solid cubic slightly curved faces meet plateau laws better solution found proposed structure adapted structure outer wall summer olympics scale living cells foam patterns common skeleton sea resemble mineral casts plateau foam boundaries skeleton beautiful marine form drawn looks sphere composed wholly impossible characteristic states convex number faces plus number corners equals number edges plus result formula closed include exactly like soccer ball dome noting flat like sheet chicken wire pentagon added forces bend fewer corners pulled patterns formed repeating tiles flat surface groups common art design exactly repeating easy find living things cells paper nests social wax cells built honey bees known examples animals bony fish reptiles fruits like protected overlapping scales form exactly repeating units scales fact vary continuously size flowers snake pattern structures minerals provide good examples regularly repeating dimensional despite hundreds thousands known minerals possible types arrangement crystal defined crystal structure crystal system point group example exactly systems dimensional space cracks cracks linear openings form materials relieve stress elastic material stretches uniformly eventually reaches breaking strength fails suddenly directions creating cracks degree joints cracks meet conversely material fails straight cracks form relieve stress stress direction simply open existing cracks stress right angles create new cracks degrees old ones pattern cracks indicates material elastic tough material like oak tree bark cracks form relieve stress usual grow long growth interrupted strong elastic species tree structure levels cell molecules pattern splitting bark spots stripes spotted striped patterns evolutionary explanation functions increase chances offspring patterned animal survive reproduce function animal patterns camouflage instance leopard harder catches prey function signalling instance likely attacked predatory birds hunt sight bold warning colours bitter poisonous insects young bird warning patterned insect like try eat soon spit bitter insect area remain young genes create survive evolutionary functional arguments explain animals need patterns explain patterns formed pattern formation later mathematical biologist described mechanism spontaneously creates spotted striped patterns reaction system cells young organism genes switched chemical signal resulting growth certain type structure patch skin present result black leopard distributed spots stripes result suggested feedback control production cause continuous fluctuations body second mechanism needed create standing wave patterns result spots stripes chemical switches production body quickly resulting scheme reaction non biological example kind scheme chemical later research managed create convincing models patterns diverse stripes jaguar spots medium dark patches surrounded dark broken rings shell patterns different spots stripes illustrations activation models developed work use account observed range basic feather patterns simplest central pigment patch concentric patches bars eye spot pair central spots rows paired spots array dots elaborate models simulate complex feather patterns guinea individual feathers feature transitions bars base array dots far end require created signals interactions space time patterns form reasons landscape tiger bush fir waves tiger bush stripes occur arid slopes plant growth limited rainfall roughly horizontal stripe vegetation effectively collects bare zone immediately fir waves occur forests mountain slopes wind disturbance regeneration trees fall trees sheltered exposed turn likely damaged gaps tend expand young trees grow protected wind shadow remaining tall trees natural patterns formed animals areas appear created years activities pocket soils active upper layer subject annual freeze patterned ground form creating circles nets ice wedge steps stripes thermal causes cracks form water fills cracks expanding form ice frozen widening cracks cracks join form shapes pioneering authors translated der art forms nature thompson growth form cambridge general books adam nature modeling patterns ball philip nature patterns parts shapes flow branches oxford murphy pat william nature design chronicle books david survival beautiful art science evolution press stevens nature stewart shape magical numbers nature patterns nature art bernard patterns earth design nature universal forms principles design new riders pattern patterns inspired nature books surfaces textures visual black porter james nature chaos viking
Patterns in nature