Medley of spirals from cyclic cellular automata

Cyclic cellular automata on the integer planar lattice are known to typically evolve through distinct phases ending with minimal periodic terminal states that usually appear as intertwined spirals. Here we explore the diversity of spirals that arise from nonstandard neighborhoods on the integer lattice and from looking at the automata on quasi-crystalline arrangements of cells. We see that phase transitions and development of spirals are almost ubiquitous yet the particular form of the spirals is very dependent upon the particulars of the underlying neighborhoods; in fact the spiral forms echo the neighborhoods. The quasi-crystalline illustrations provide much more subtle echoes in the spiral forms that show artifacts from the non-periodic local symmetry that occurs.

Title	Medley of spirals from cyclic cellular automata
Creator	Reiter, Clifford A.
Publisher	Computers and Graphics
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	February 2010
Date Available	2015-04-17T18:29:06Z
Type	Article
Language	English
Keyword	phase transition
	quasi-crystals
	automata
	self organization
	cyclic state automata
Bibliographic Citation	Reiter, C. A. (2010 Feb.) "Medley of spirals from cyclic cellular automata." Computers and Graphics 34 (1): 72-6.
Standard Identifier	Handle 10385/1799
Standard Identifier	DOI 10.1016/j.cag.2009.04.008
Permalink	http://hdl.handle.net/10385/1799
Rights Statement	In Copyright
Rights Holders	Elsevier Ltd.