10.6092/issn.1973-9494/9992
El Tajín was an ancient metropolis in which rituals such as the Mesoamerican ball game were carried out, later to be recorded in the sculptural bas-reliefs of its architecture. The study of its morphologies is the recognition of the ways in which an ancient civilization is expressed, thus contributing to the characterization of a culture whose past belongs to World Heritage. This paper proposes a case-sample analysis of the bas-reliefs in the South Ballcourt based on reticular geometry and fractal dimension analysis. It was found that the geometry of the RA (golden rectangle), RR2 and RR3 are prevalent, in addition to the identification of iconographic naturalist and symbolic elements; from the box-counting fractal dimension, it was found that the elements, though of different sizes or composition, show similar complexities, with a value of around 1.7.
application/pdf
1973-9494
9992
en
Edgardo J. Suarez-Dominguez
Conservation Science in Cultural Heritage
fractal dimension
A Study of the Formal Architectural-Sculptural Characteristics of El Tajin
Text.Serial.Journal
https://conservation-science.unibo.it/
19
Articles
2020-03-18
2019-11-12
2020-03-18
2020-03-18
143-156
CSCH
Edgardo J. Suarez-Dominguez
2019
10.6092/issn.1973-9494/9992
143
Universidad Autónoma de Tamaulipas
1973-9494
fractal dimension
en
156
A Study of the Formal Architectural-Sculptural Characteristics of El Tajin
https://conservation-science.unibo.it/article/download/9992/10604
19
A      STUDY OF THE FORMAL ARCHITECTURAL-
       SCULPTURAL CHARACTERISTICS OF EL TAJIN

    Lorena G. Valle-Chavarria*, Carlos E. Berumen-Rodriguez, Edgardo J. Suarez-
    Dominguez•1
    Facultad de Arquitectura, Diseño y Urbanismo, Universidad Autónoma de Tamau-
    lipas, México




    Keywords: visual language, world heritage, architectural design, fractal dimension


    1. Introduction

    Located on the coast of the Gulf of Mexico and comprising an area of 144 hec-
tares of architectonic buildings, El Tajin was the pre-Hispanic ceremonial center with
the highest level of development during the late Classic period, between the years
600-900 [1].
    Since its beginnings, the architecture-sculpture of El Tajín1 has stood out for its use
of formal, overlapping elements on its buildings which highlight the importance of the
rituals to which they refer, be they of life or of death [2].
    The ritual which stands out the most is the Mesoamerican ball game2. Until now,
twenty ballcourts for practicing this ritual have been found [3]. The survival of this ritual
to the present day demonstrates its deep cultural significance [4].
    Upon the court walls one can see sculptured, intricately designed bas-reliefs dis-
playing a formal, well-defined pattern organized in a style known as Classical Verac-
ruz, which implies a preoccupation with aesthetics, regularity of shapes, and a flair for
ornamentation [5].
    The formal architectonic-sculptural structure reveals a geometric and mathematical
organization within a parallel system between architectonic thought and mathematical
conception [6].
    Identifying the geometric pattern implies recognizing the relationships between pro-
portionality, similarity, scale, surroundings and constants [7] pertaining to a visual lan-
guage related to myths and religion.
    The author Bertels, recognized characters and deities belonging to this culture in
the bas-reliefs [8]. As such, the recognition of forms is important for the characteriza-
tion of a culture because it is a way to determine and learn more about its identity. The
present work, therefore, attempts to show a structural morphology explained through
geometry, complementing the study with the concept of fractality.

*   Corresponding author: lvalle@uat.edu.mx; edgardo.suarez@uat.edu.mx
                                                                                                                 The concept of fractals more rigorously explains the formal constants and com-
                                                                                                             position that give unity to a work of art, while another fractal dimension is presented
                                                                                                             through formal auto-similarity [9].
                                                                                                                 In Meso-American architecture, one can observe the formal superimposition of rep-
                                                                                                             etition in the different scales of the patterns generated by the building’s structure.
                                                                                                                 As such, the results offer a new focus on the recognition of art forms in which one
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                             finds thought and cosmovision materialized in the culture of El Tajín, a UNESCO world
                                                                                                             heritage site.


                                                                                                                2. Method

                                                                                                                To begin study of the panels’ geometric patterns, the El Tajín Sculpture Catalogue
                                                                                                             by Patricia Castillo [10] was used as a reference. From this, high-quality photostatic
                                                                                                             B/W copies of the sculptural panels’ linear drawings of the South Ballcourt were ob-
                                                                                                             tained to better visualize them.
                                                                                                                For this study, the Northwest Panel and the South-Central Panel of the South Ball-
                                                                                                             court were chosen, as they are considered to be the most important of the site, mainly
                                                                                                             due to the profusion of images contained in the bas-reliefs of their panels.
                                                                                                                Experimental grids were carried out on photostatic copies of the sculptural panels’
                                                                                                             linear drawings to identify an organization of regular geometric patterns, employing
                                                                                                             manual instruments including a precision compass, squares and rulers.
                                                                                                                This method has already been applied to other buildings in El Tajin [11].
                                                                                                                Once a regular pattern analogy was identified using the square/rectangle, golden
                                                                                                             rectangle (RA/Φ), square root rectangle (RR2) and cube root (RR3) relationships, the
                                                                                                             obtained pattern was drawn describing the method in the following way, employing let-
                                                                                                             ters to identify geometric reference points.


                                                                                                                2.1. Northwest panel (South ballcourt)

                                                                                                                 Figure 1 - GR-General Rectangle: ABCD composed of RR2 with CE radius and C-
                                                                                                             center, an arc is drawn at point D.
                                                                                                                 EBFD delimits the area containing the skeleton character with large headdress.
                                                                                                                 RR2: with DG radius and D-centre, an arc is drawn at point C, in which the straight
                                                                                                             line GH marks the central axis of the ball player character with headdress.
                                                                                                                 RR2: with NG radius and center in N, an arc is drawn at point J, marking the width
                                                                                                             of the panel’s upper frieze.
                                                                                                                 Its golden section Φ with the straight lines KK’, MM’ is obtained from the straight line
                                                                                                             JC. The faces of all the characters in the panel are found lined up in this area.
                                                                                                                 The golden proportion Φ of the straight line JQ is point P. The straight line PP’ marks
                                                                                                             the central axis of the anthropromorphic human/canine form.




                                                                                                       144
           Figure 1. Geometric pattern, Northwest panel, South Ballcourt. El Tajín,



  2.2. South central panel, south ballcourt




                                                                                                  CONSERVATION SCIENCE IN CULTURAL HERITAGE
    Figure 2 - From the GR-General Rectangle: ABCD, 2 RR3 overlapping, with HJ ra-
dius and H-center an arc is drawn at point C and with radius GK and G-center an arc
is drawn at point D.
    The straight line AC and the straight line GH are divided into four equal parts mark-
ing important points within the composition of the panel.
    The width of the upper frieze is obtained with RA; with PQ radius and P-center an
arc is drawn at point R and and that of the bottom frieze with RR2; with ST radius and
S-center an arc is drawn at point U.
    The RR3: with HJ radius and H-center an arc is drawn at point C and with GK radius
and G-center an arc is drawn at point D; determine the width of the decorative outer
vertical strips.
    The RA (Փ): with radius O’E and center in O’ an arc is drawn at point V and with
radius O’F with center in O’ an arc is drawn at point W; determine the vertical strips
followed by the outer strips.




                                                                                            145
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                                   Figure 2. Geometric pattern, south central panel/south ballcourt, El Tajín, México.



                                                                                                                The RR2: with HE radius and H-center an arc is drawn at point L and with radius GF
                                                                                                             and G-center an arc is drawn at point M; are the width of the next strips ordered from
                                                                                                             outside to inside.
                                                                                                                The fractal dimension D was determined by making use of the ImageJ v1.46 pro-
                                                                                                             gram [12] through the relationship [13]:




                                                                                                               Where (r) is the size of the N sites in which the image is divided and N0 is the num-
                                                                                                             ber of sites in which the presence of precipitates is observed.
                                                                                                               If one takes into consideration that D constitutes a measure of the quantity of an
                                                                                                             occupied space Φ which is found on a longitudinal plane, characteristic L:




                                                                                                             it is to be expected that the value of D increases with the amount of precipitate
                                                                                                             formed.
                                                                                                                 Fractal geometry has been used to determine architectonic characteristics [14]. In
                                                                                                             addition to studies of roughness [15], it has also been applied to paintings.
                                                                                                                 Different methodologies have been presented, with computer simulation as a first
                                                                                                             option, and size effects and theoretical analysis among others [16], using building
                                                                                                             scales that can be studied at the microscopic level.

                                                                                                       146
   To determine fractality, photographs were taken of the panels. The surface area of
the images was calculated using the fractal dimension method by LCD screen and the
ImageJ v1.4g program in which each color image is converted to an 8-bit image. From
this, a binary image of the pattern showing the exterior borders of the surface area was
obtained. Thus, vertical and horizontal fractal dimensions of the images, as well as
their texture, were acquired (Figures 3, 4 and 5).
   Similar methods were reported by other authors where box-counting fractal dimension is
used to characterize image and determine relationship in lines that compounds itself [17-18].




a                                                   b
Figure 3. Photograph of the northwest panel; a) original image; b) binary image.




                                                                                                                CONSERVATION SCIENCE IN CULTURAL HERITAGE
a                                                   b
Figure 4. Photograph of the south-central panel before restoration; a) original image; b) binary image.




a                                                   b
Figure 5. Photograph of the south-central panel after restoration; a) original image, b) binary image.

                                                                                                          147
                                                                                                               3. Discussion

                                                                                                                General observations regarding the geometric composition of the panels.
                                                                                                                The reticular rectangular structure that predominates in the design of the pan-
                                                                                                             els adjust appropriately to the general model architecture of ballcourts; the bas-
                                                                                                             reliefs are sculpted in the walls, invariably located at the foot of the court, at the
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                             so-called benches, which are the closest for the participants in the ritual ballgame
                                                                                                             (the players). One may deduce that their design, proportion, morphology and se-
                                                                                                             miotics were meant to establish visual contact directed toward a specific objective
                                                                                                             in the first instance, since in addition to the players, other characters intervened
                                                                                                             including priests, high-ranking persons, etc.
                                                                                                                The interlocking pattern characteristic of the Classic Veracruz style found in
                                                                                                             the panels, are usually located on the vertical and horizontal strips, although they
                                                                                                             also appear in the friezes as a border in the corners, intermixed with other motifs,
                                                                                                             etc. The visual technique utilized in the strips is the rhythmic repetition of motifs
                                                                                                             interlocked in horizontal and vertical sequences, occupying an important space in
                                                                                                             the general visual field of the panels.
                                                                                                                The volutas and interlocking are the unifying graphic motif of the panels’ com-
                                                                                                             position due to its insistent presence in all the friezes, vertical strips, clothing and
                                                                                                             headdresses of the characters. In the semiotics field, they function as basic signs
                                                                                                             or lexemes belonging to an ancient codifying system as proposed by Pascual
                                                                                                             Soto. This researcher has studied the morphosyntactic structure by identifying
                                                                                                             the formal regularities of the signs and their combinatorial order, as well as their
                                                                                                             semantic value [19].
                                                                                                                Within the compositional structure, the upper frieze leads the panel scenes, in
                                                                                                             which can be observed the faces of deities and mythical signs.
                                                                                                                There is a tendency to orient the composition toward the center of the square or
                                                                                                             rectangle, so that our vision is drawn to the specific scenes that occur at that point.
                                                                                                             Within the complexity and dynamism of the images, order and balance is achieved
                                                                                                             between the horizontal and vertical axes of the composite skeleton. The geometric
                                                                                                             pattern found in the panels are: RA (Փ), RR2, RR3.
                                                                                                                The motif repeated in all the panels, as much in the North Ballcourt as in the
                                                                                                             South Ballcourt, is the eye with volutas, highlighted in Figure 6.
                                                                                                                As for the position it occupies within the panels, it is visible:
                                                                                                                • in the upper frieze
                                                                                                                • as a base in the ascending/descending or east/west scenes
                                                                                                                • as a part of the character’s headdress
                                                                                                                • in rhythmic repetition within the vertical strips.




                                                                                                       148
    Figure 6. Northwest panel /south ballcourt in which 5 eyes with volutas are highlighted



  The different graphic representation variables are:
  • with stylized feathers as a border, or in the characters’ ritual costume adornment
  • with volutas as a border.
  Another constant motif is that of the ollín3, meaning movement, that normally ap-




                                                                                                    CONSERVATION SCIENCE IN CULTURAL HERITAGE
pears in the characters’ costumes; it can also be observed in the friezes and at the
base of the panel scenes (Figure 7).
  • In the clothing: in the waistband and in the bags of copalli4




                   Figure 7. Clothing details from the south ballcourt panel




                                                                                              149
                                                                                                             • In the frieze (Figure 8).
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                                             Figure 8. Details in the frieze of the south ballcourt panel



                                                                                                             • At the bottom of the panels (Figure 9).




                                                                                                                                     Figure 9. From the south ballcourt panel



                                                                                                             The anthropomorphic characters are:
                                                                                                             • human/bird, human/dog, human/rabbit according to Piña Chan (Figure 10).




                                                                                                                                     Figure 10. From the south ballcourt panel




                                                                                                       150
   The flora and fauna represented include the maguey plant, turtle, stylized serpents
with precious feather adornments and an eye with volutas for eyelids (Figure 11).




                    Figure 11. Maguey plant, turtle, interlocked serpents



    The description of the naturalist and symbolic elements composing the panels was
also facilitated by the reticular organization of their composite geometry, which re-
vealed a formal order responding to a particular cosmic worldview of their ritual and
religious thought.
    Fractal proportionality presents the following characteristics:
    • Geometric composition and dimensioning linked to sacred and astronomical
numerology provided ancient American cultures with a highly rigorous scientific
vision [20].
    • Mandelbrot established that a fractal is a special kind of symmetry or invariance,
that relates a whole to its parts and the whole can be broken down into parts that evoke
the whole [21].




                                                                                                   CONSERVATION SCIENCE IN CULTURAL HERITAGE
    • The harmonic proportion systems of pre-Hispanic images lead us to fractal geom-
etry. The interpretation is a result of the Mandelbrot method described in the previous
paragraphs.
    • Non-Euclidian geometry, also known as fractal geometry, allows for a broadening
of the understanding of the processes of morphogenesis as another way to observe
existing reality [22].
    • Since a fractal is a geometric construction, as a shape in space, it is possible to
show the fractal in the geometric constructions made by man, such as population sites,
architecture and art [23].
    • The contribution of fractal geometry as a generating instrument gives architecture
the power to simultaneously express two seemingly contradictory states: orderly forms
and organic complexity [24].
    • A fractal organization happens when there is a motif or a regular design that re-
peats itself as it grows or changes its scale.
    • The value of the fractal dimension in a system can vary depending on the dynamic
processes taking place and its random nature by which one can describe a system
through its morphology. In this work, the morphologies correspond to the images ob-
tained through the previously described experiments.
    Table 1 shows the results of fractal dimension analysis for the borders of the reliefs
in the studied areas.


                                                                                             151
                                                                                                             Table 1. Fractal dimension results for case-study panels

                                                                                                                                              OBSERVATION                FRACTAL          ERROR
                                                                                                                                                                        DIMENSION
                                                                                                                 Northwest panel         Elaborate curvatures can         1.612            0.081
                                                                                                                                         be observed representing
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                                                         the main ball players.
                                                                                                               Central south panel       The     most    elaborate        1.683            0.045
                                                                                                               (before restoration)      curved shapes highlight
                                                                                                                                         the larger dimensions and
                                                                                                                                         major visual morphology.
                                                                                                               Central south panel       Defined elements                 1.701            0.085
                                                                                                                (after restoration)


                                                                                                                 As one can see, the values differ by less than 7%, and considering the margins of
                                                                                                             error, no significant differences were found among the results.
                                                                                                                 Formally, the fractal dimension values qualitatively express that the elements stud-
                                                                                                             ied have similar complexity. Indeed, the set of combined elements present a set of
                                                                                                             more elaborate curvatures compared to other elements such as the volutas, which
                                                                                                             tend to present linear geometric shapes or simpler geometric combinations.
                                                                                                                 The previously described fractal dimension is obtained mathematically through a re-
                                                                                                             lationship between individual elements with a topographic dimension and the number
                                                                                                             of times they fit within a figure.
                                                                                                                 In this sense, the images studied for El Tajín show a fractal dimension, that is,
                                                                                                             complexity in the arrangement of the lines that form the picture.
                                                                                                                 The study shows the fractal dimension value is reduced in the images with the de-
                                                                                                             graded figures and is increased when those figures are restored. This indicates, there-
                                                                                                             fore, that for the case in question, the mathematical complexity diminishes with time due
                                                                                                             to the degradation of the figures, which is coherent with what can be observed visually.
                                                                                                                 On the other hand, in the studies undertaken for the images it was found that the
                                                                                                             results contained no significant differences, but they did appear in the other experi-
                                                                                                             mental cases of different figures studied for the same ceremonial center. This situation
                                                                                                             was also found in the study by means of quadratic relations in which they had differing
                                                                                                             geometric dispositions but where an RR2 relationship also prevailed and is a deriva-
                                                                                                             tion of the golden rectangle.
                                                                                                                 As such, when the study shown in this work was carried out with pre-Hispanic ves-
                                                                                                             tiges, the conserved elements displayed a fractal dimension. Even though in Mesoa-
                                                                                                             merican cultures, the term ‘fractal dimension’ was unknown, this mathematical geom-
                                                                                                             etry could have been instinctively applied not only to relate to in a divine sense, but
                                                                                                             also with the natural use of profound logical reasoning. In this regard, Dehouve affirms
                                                                                                             that, in Mesoamerica, the plastic forms of fractal nature are generally widespread [23].
                                                                                                                 As such, when the study shown in this work was carried out with pre-Hispanic
                                                                                                             vestiges, the conserved elements display a fractal dimension. Even though in Mes-
                                                                                                             oamerican cultures, the term ‘fractal dimension’ was unknown, its mathematical ge-
                                                                                                             ometry could have been instinctively applied to relate in the divine sense. In this
                                                                                                             sense, Dehouve affirms that in Mesoamerica, the plastic forms of fractal nature are
                                                                                                             generally widespread [23].


                                                                                                       152
    4. Conclusions

   Formal resources were placed in function and at the disposition of the ritual concept.
   The formal organization of architecture-sculpture in El Tajín is a means of
identitying its culture. Involving architectonic spatiality in a temporary context is
something which we can access only with difficulty because there are no written
testimonials, but with multi-disciplinary studies that complement this research, cri-
teria for a better interpretation and characterization of this ancient culture could
be achieved.
   In composite geometric analysis, the square root rectangle (RR2) prevails as
the most constant pattern. The golden rectangle and the cubic root rectangle are
also employed, having the square root as its initial base, which in Mesoamerican
cultures, represents the four cardinal points.
   Geometric relationships are in accordance with the proportions and scales of
the formal elements of which they are composed.
   In architectural works, fractal geometry is observed in patterns of formal simi-
larity that are repeated in different scales; the form and identity of the building
are understood through the formal interactions of the compositional structure: the
whole with its parts.
   Fractal patterns may or may not have been used intentionally in El Tajin, how-
ever, there remains the fact that fractal values were found in its buildings.
   Taken together, the formal considerations resulting from the visual semantics
and interpretation of the panels carried out in this study, will complement and add
to the current knowledge of the cultural heritage of El Tajin.
   Fractal and Euclidian geometry complement each other to generate new perti-
nent models for the study of ancient art. As in nature, form is the complement of
function. Hence, forms have a reason for being, and it is because of them that the
study of formal composition helps bring us to a better understanding and percep-




                                                                                                            CONSERVATION SCIENCE IN CULTURAL HERITAGE
tion of cultural vestiges.


    Acknowledgments

    EJSD wishes to thank PRODEP for support for NPTC 511-06/18-9249.


    Notes

1
      whc.unesco.org/en/list/631/video
2
      The Mesoamerican ballgame was a ritual/sport played from 1800 B.C. There were differ-
      ent versions of the ritual/sport in different places during the millennia and today, a newer,
      more modern version of the game, ulama, is still played in a few places by the indigenous
      population.
3
      According to the Nahuatl dictionary, ollin means “movement.” For the Aztecs it is the mysti-
      cal sign of the Lord of Movement called Ehecatl.
4
      In pre-Hispanic times, among the Mexicans or Aztecs, it was known as copalquáhuitl:
      “copal tree”, and the resin extracted from it as copalli: “incense”. the Mexicans used it for
      their rituals.



                                                                                                      153
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     de espacios residuales con anclaje emocional en el inconsciente particular y
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   Biographical notes

   Lorena Gertrudis Valle Chavarria, full-time research professor at the Autonomous
University of Tamaulipas, Bachelor of Graphic Design, Faculty of Arts and Design
UNAM, México, master’s degree, University of Salamanca, Spain and PhD in Preser-
vation and Restoration of Historical-Artistic Heritage at the Universitat Politecnica de
Valencia (UPV), Spain. Her field of research focuses on the management of cultural
heritage related to art, architecture and graphic design.




                                                                                                   CONSERVATION SCIENCE IN CULTURAL HERITAGE
   Carlos Eric Berumen Rodriguez, full-time research professor at the Autonomous
University of Tamaulipas, Bachelor of Architecture, by Faculty of Architecture, Design
and Urbanism, Tamaulipas, México, Master Degree, University of Salamanca, Spain
and PhD in Preservation and Restoration of Historical-Artistic Heritage at the Univer-
sitat Politecnica de Valencia (UPV), Spain. His field of research is the management of
cultural heritage related to art, architecture and sculpture.

   Edgardo Jonathan Suarez Dominguez, Bachelor of Industrial Chemistry and Ar-
chitect, Master Degree in Engineering, PhD in Administration and PhD in Mechanical
Engineering. Full-time research professor at the Autonomous University of Tamaulipas.
Edgardo does research in Mechanical Engineering, Solid-state Chemistry and Electro-
chemistry. A current project is ‘Extraheavy crude oil transport enhancer’, EOR and new
materials development. An SNI member, he is also a member of the Society of Petro-
leum Engineers, the Mexican Society of Physics and the Chemical Society of Mexico.


   Summary
   El Tajín was an ancient metropolis in which rituals such as the Mesoamerican ball
game were carried out, later to be recorded in the sculptural bas-reliefs of its architec-
ture. The study of its morphologies is the recognition of the ways in which an ancient


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                                                                                                             civilization is expressed, thus contributing to the characterization of a culture whose
                                                                                                             past belongs to World Heritage. This paper proposes a case-sample analysis of the
                                                                                                             bas-reliefs in the South Ballcourt based on reticular geometry and fractal dimension
                                                                                                             analysis. It was found that the geometry of the RA (golden rectangle), RR2 and RR3 are
                                                                                                             prevalent, in addition to the identification of iconographic naturalist and symbolic ele-
                                                                                                             ments; from the box-counting fractal dimension, it was found that the elements, though
L.G. Valle-Chavarria, C.E. Berumen-Rodriguez, E.J. Suarez-Dominguez - A study of the formal architectural




                                                                                                             of different sizes or composition, show similar complexities, with a value of around 1.7


                                                                                                                Riassunto
                                                                                                                El Tajín era un’antica metropoli in cui venivano eseguiti rituali come il gioco della
                                                                                                             palla mesoamericana. Questo gioco è riportato, a livello architettonico, su bassorilievi.
                                                                                                             Lo studio delle modalità espressive di un’antica civiltà contribuisce alla caratterizza-
                                                                                                             zione di una cultura, il cui passato appartiene al Patrimonio Mondiale. Questo articolo
                                                                                                             propone un’analisi del caso di studio dei bassorilievi nel South Ballcourt basata sulla
                                                                                                             geometria reticolare e l’analisi della dimensione frattale. Si è riscontrato che prevalgo-
                                                                                                             no la geometria di RA (rettangolo aureo), RR2 e RR3. Oltre all’identificazione dell’ico-
                                                                                                             nografia e degli elementi simbolici dei bassorilievi, dalla dimensione frattale di conteg-
                                                                                                             gio delle caselle si è scoperto che gli elementi, sebbene di dimensioni o composizione
                                                                                                             diverse, mostrano complessità simili, con un valore di circa 1,7.




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