Plane–and Space–Filling Trees by Means of Chain Coding

E. Bribiesca*¹, N. Espinosa–Dominguez²

^1,2 Department of Computer Science, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas Universidad Nacional Autónoma de México Apdo. Postal 20–726, México, D.F., 01000. Fax: (5255)5622–3620 *E–mail: ernesto@leibniz.iimas.unam.mx

ABSTRACT

An algorithm for constructing fractal trees is presented. Fractal trees are represented by means of the notation called the unique tree descriptor [E. Bribiesca, A method for representing 3D tree objects using chain coding, J. Vis. Commun. Image R. 19 (2008) 184–198]. In this manner, we only have a one–dimensional representation by each fractal tree via a chain of base–five digit strings suitably combined by means of parentheses. The unique tree–descriptor notation is invariant under rotation and translation. Furthermore, using this descriptor it is possible to obtain the mirror image of any fractal tree with ease. In this paper, we focus on fractal plane–filling trees and space–filling trees.

Keywords: Fractal trees, tree descriptor, plane–filling trees, space–filling trees, chain coding.

RESUMEN

Se presenta un algoritmo para la construcción de árboles fractales. Un árbol fractal es representado por medio de la notación llamada descriptor único de árboles [E. Bribiesca, A method for representing 3D tree objects using chain coding, J. Vis. Commun. Image R. 19 (2008) 184–198]. De esta manera, se tiene solamente una representación unidimensional para cada árbol fractal por medio de una cadena de digitos de base cinco adecuadamente combinados por medio de paréntesis. La notación del descriptor único de árboles es invariante bajo rotación y traslación. Además, usando este descriptor es posible obtener la imagen especular de cualquier árbol fractal con facilidad. El contenido de este artículo se enfoca en el estudio de los árboles fractales que cubren el plano y el espacio.

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