Geometric and Complex Analyses of Maya Architecture: Some Examples

Originating in the Yucatan Peninsula, the ancient Maya civilization occupied a vast area of Mesoamerica between 2600 BC and 1200 AD. Constructing thousands of architectural structures and developing sophisticated concepts surrounding the disciplines of astronomy and mathematics, the Maya civilization rose to a cultural florescence between the years 600-800 AD. Although this prosperity reigned for nearly two centuries, the Maya civilization met with misfortune between 800-900 AD. In order to gain an interpretative perspective on the fractal analysis of complex geometry and mathematics of Mesoamerican architecture, this paper contemplates two procedures to describe fractality and the fractal dimension (Df). In the first procedure sixteen pyramids were analyzed. The authors studied a data set that was treated has a fractal profile to estimated the fractal dimension (Df) through variography (Dv). The estimated Dv = 1.236. In the second procedure, fourteen pyramids were included and the estimated Fractal Dimension Dv = 1.312. In the third procedure, twenty-six pyramids were deciphered and saved as bitmap files. These images were analyzed with the program "Benoit" in order to calculate Box (Db), Information (Di) and the Mass Dimensions (Dm). The estimated general averages were Db = 1.931, Di = 1...941 and Dm = 1.959. This type of study indicates a relationship between the cosmological setting and myth.

ABOUT THE AUTHORS
Gerardo Burkle Elizondo: Human Medicine, 1973-78, School of Medicine, Universidad La Salle, México D.F. Residence in Internal Medicine, 1979-82, Instituto Nacional de La Nutrición, México D.F. Master in Phylosophy, 1989-92. Universidad Autónoma de Zacatecas, México. Doctorate Ph-D in History, 1999-2004. Universidad Autónoma de Zacatecas, México. Several publications about Fractal and Chaos Theory applied to Mesoamerican Art and Architecture, from 2001 to 2004. Author of a book about Chaos Theory and Medicine and Psychology published by the University of Zacatecas, 1999.

Nicoletta Sala has received her degree in Physics, applied cybernetics, at State University of Milan, Italy. Ph-D in Communication Science at Università della Svizzera italiana of Lugano, Switzerland. Postgraduates (each two years) in :"Didactics of the communication and multimedia technologies" and "Journalism and mass media". She teaches Mathematics Thought and Computer Graphics and New Media at the Academy of Architecture of Mendrisio, Switzerland. She is co-editor of the Chaos and Complexity Letters International Journal of Dynamical System (Nova Science, New York). She studies the interconnection between mathematics, fractal geometry and architecture. She has written 14 mathematics and information Technology textbooks and several scientific papers dedicated to the complexity and fractal geometry in arts and architecture.

Ricardo Valdez-Cepeda: Engineer in Agronomy. Master and Doctor PhD. in Agronomy. He applied the fractal geometry in different research fields. He works at the Universidad Autónoma Chapingo (Mexico).

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