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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Computational Methods for Juxtaposition Fractals
by
Valentin Boju
Univ. of Craiova
Coauthors: Louis Funar (Univ. de Grenoble I)

In this paper is presented a class of fractals obtained using the juxtaposition function, hF, defined, [1], for a topological disk F subset or equal Rn, and a symmetry with respect to \partialF. For each \lambda in (0, 1], consider a maximal collection { Fp, p = 1, ..., hF(\lambda) } of sets with disjoint interiors, homothetic to F in ratio \lambda, which have only boundary points in common with F. For each Fp, let wp be the similitude which sends F into Fp. We call the attractor of the IFS { En ; wp , p = 1, ... , hF(\lambda) } the juxtaposition fractal (JF) associated to F, with parameter \lambda. The method is valid for both variants of the juxtaposition function. Combining the two variants of this function in a random manner we obtain a random juxtaposition fractal (RJF). Next we consider another variant of the juxtaposition function defined for two topological disks K, G subset or equal En and the corresponding JF associated to K and G.

Some properties regarding the fractal dimension of the JF are given. There are also given the IFS codes corresponding to the JF obtained for some pairs (K, G) of elementary patterns.

Next, using as generator for juxtaposition a symmetric convex disk G, it is presented a method for increase the measure of convexity of a concave topological plane disk K. An algorithm for the case when K itself is a polygon is given.

The RJF method has a special interest in biology since it can provide a growth model in hystology.

[1]
V. Boju, L. Funar, Gerenalized Hadwiger numbers for symmetric ovals. Proc. Amer. Math. Soc., Vol 119, Nr. 3, 1993, pp. 931-933.

Date received: April 12, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caae-05.