Spiral Dragon: rule (B23/S/Cx,x=4, 5, ...) on kite and dart Penrose tilings

Several configurations of B23/S/C5 and B23/S/C4 are included in this movie.

Normally, spirals generated by such simple life-like cellular automata (CA) on a square grid have quite "artificial" looks (e.g. B234/S2/C5 http://psoup.math.wisc.edu/mcell/rules/gene_spirals.gif ). Even in the case of more complicated cyclic CA families, the variety of initial configurations is inevitable to get the variety of patterns (cf. http://psoup.math.wisc.edu/mcell/rullex_cycl.html ).
But in the case of Penrose tilings, thanks to the quasi-periodic features of the cellular space, just starting from a small seed (two live cells), it is possible to get some kind of distinct spiral patterns, including right spin and left spin.

The meaning of parameters B,S and C is described in Cellular Automata rules lexicon page ( http://psoup.math.wisc.edu/mcell/rullex_gene.html ).
Refer to the following document for cellular automata on Penrose tilings
Owens and Stepney (2008) http://www-users.cs.york.ac.uk/susan/bib/ss/nonstd/auto08b.pdf

Category:

Science & Technology

Tags:

• cellular
• automata

[CARule110]

Very nice spirals!

So, significantly different of square and hexagonal.