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Fractal geometry in Mesoamerica. (English) Zbl 1202.01009

Summary: Fractal Dimension in different groups of mesoamerican artistic and architectural works was quantified in 106 structures. To make the analysis we used the “Benoit” program in order to calculate “Box Dimension”, “Information Dimension”, “Mass Dimension” and “Y” value about “Fractal Dimension”. We found a general average of 1.92 for fractal dimension with values by groups in a range between 1.883 and 2.038. These results are in a very good agreement with the fact that the values of complex fractals are usually situated between 1.5 and 2.0. Fractal dimension shows the efficiency with which an object fills the space that contains it, and is quantificated like the morphology of their complexity.
Scaling properties exponent were proved, and specifically the fractal dimension obtained looks like a possible pattern. We think that part of the simple rules that could explain these complex dynamics findings is the fact that the artists and architects in Mesoamerica used mathematics in their work. The finding of “proportional systems” and “golden units” to measure in modular forms, like scaling rectangles and other techniques to get harmonic and constant units in the case of Mesoamerica, had been proved by some authors.

MSC:

01A07 Ethnomathematics (general)
28A80 Fractals
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