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Some classes of self-similar planar fractals

Dušan Pagon

Faculty of Education
University of Maribor, Maribor, Slovenia

We present some well known classes of planar fractals, based on regular polygons, and introduce a new class of fractals, appearing from the construction of simple branching trees. Most of the studied objects are self-similar in a strong sense. Therefore, the self-similar dimension $d_S={\ln N\over\ln k}$, where $N$ is the total number of congruent sub objects and $k$ is the coefficient of similarity, is introduced and its properties are studied. Besides the dimension $d_S$, various other characteristics of the presented fractals are examined, for instance, when the overlapping occurs, what is the equation of the boundary curve, and what is the density of the embedded object. We also explain the concept of an iterated function system and give the IFS-codes for some of the studied fractals. Most of the results can be generalized to the 3-dimensional space (starting, for instance, with regular solids) and into the higher dimensions.

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next up previous
Next: Pichard Up: Abstracts Previous: Nakamura