Geodesic
Periodic Fractal Patterns
Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 1-6.

Voir la notice de l'article provenant de la source Heldermann Verlag

We present an algorithm that can create patterns that are locally fractal in nature, but repeat in two independent directions in the Euclidean plane - in other word "wallpaper patterns". The goal of the algorithm is to randomly place progressively smaller copies of a basic sub-pattern or motif within a fundamental region for one of the 17 wallpaper groups. This is done in such a way as to completely fill the region in the limit of infinitely many motifs. This produces a fractal pattern of motifs within that region. Then the fundamental region is replicated by the defining relations of the wallpaper group to produce a repeating pattern. The result is a pattern that is locally fractal, but repeats globally a mixture of both randomness and regularity. We show several such patterns.
Classification : 28A80, 51F99
Mots-clés : Fractals, wallpaper groups, algorithm 
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D. Dunham; J. Shier . Periodic Fractal Patterns. Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 1-6. http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a0/