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Title: Árboles fractales binarios simétricos autocontactados y sus geometrías contenidas
Author: Cruz Banegas, Manuel Omar
Tutor: Garijo Real, Antonio
Keywords: fractal tree
fractal dimension
Issue Date: 20-Jun-2021
Publisher: Universitat Oberta de Catalunya (UOC)
Abstract: In nature there are many objects that can be described with classical geometry, but some such as trees do not admit a simple explanation and have to delve into fractal geometry, that is, deal with structures that are repeated at different scales. This work concerns binary fractal trees obtained symmetrically, classifying them according to the type or absence of contact in their branches, emphasizing self - contacting trees and their respective canopy, which is a fractal curve formed by points that can be accessed approaching the tree "from above". Each tree is defined by the critical contraction relationship for consecutive branches and the symmetric branching angle, data with which the so-called Mandelbrot Set for symmetric binary fractal trees is constructed, where meritorious observations of attention are perceived. The structure of each tree is graphically analyzed in all angle ranges, detailing the classical geometries contained in them and they are linked to other more complex fractal geometric sets. Special analysis is given to the golden number and the generation of the existing "golden" trees with their golden geometries included. Finally, the fractal dimension of the set of points of each tree is graphically verified and, respectively, the dimension of the canopy is analyzed mathematically using the Moran Equation at each angle, finding that the dimension of the tree canopy is always less than the dimension of the set of respective tips, since the canopy is a subset of the tree itself.
Language: Spanish
Appears in Collections:Bachelor thesis, research projects, etc.

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