Geodesic
General Rules of Fractals Construction from Polyhedra
Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 129-137 Cet article a éte moissonné depuis la source Heldermann Verlag

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The paper presents a method of construction of deterministic fractals based on uniform polyhedra using a contraction mapping procedure and an iterated function system algorithm. It was shown that the contraction mapping procedure, which implies the construction of fractals with non-overlapped and non-disjointed contractions, could produce only a limited number of fractals from uniform polyhedra, which is resulted by geometric specificity of some uniform polyhedra. The lists of uniform polyhedra from which fractals either can be constructed and not were presented and discussed. The contraction ratios and fractal dimensions of the constructed fractals were determined, some of uniform polyhedra-based fractals were presented graphically.
Classification : 51M20, 28A80
Mots-clés : Fractals, uniform polyhedra, iterated function systems, contraction mapping 
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     author = {A. Katunin and D. Kurzyk },
     title = {General {Rules} of {Fractals} {Construction} from {Polyhedra}},
     journal = {Journal for geometry and graphics},
     pages = {129--137},
     year = {2012},
     volume = {16},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a1/}
}
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A. Katunin; D. Kurzyk . General Rules of Fractals Construction from Polyhedra. Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 129-137. http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a1/