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2012 August 25

Life Variants
Penrose tilings and Ready

My apologies for the lack of recent postings. There are rumours that the LifeNews server may be turning off in the immediate future, so I was tentative about uploading something new. Nevertheless, Andrew Trevorrow convinced me that this deserves to be published on ConwayLife.com, and I understand this to currently be the most direct way of doing so.

The developers of Golly have recently turned their attentions to creating a new piece of software capable of supporting reaction-diffusion systems and cellular automata on arbitrary meshes. This has been discussed on Complex Projective 4-Space and The Aperiodical, amongst other places.

There has also been some work on cellular automata on Penrose tilings. Nick Owens and Susan Stepney investigated B3/S23 a while ago, writing a chapter about the topic in Adamatzky's Game of Life Cellular Automata. This summer, a couple of related, independent and almost simultaneous discoveries were made. One of these was a weakly universal cellular automaton on a Penrose tiling; the other was a glider.

The glider attracted a lot more attention, not least because a $100 prize was offered for its discovery. Again, this was mentioned on Complex Projective 4-Space, New Scientist and The Aperiodical. Even more recently, it was investigated on the kite-and-dart Penrose tiling, where it follows fractal paths and symmetrical loops. An image is displayed below:

The lengths of loops (half the period of the resulting oscillators, since the glider is c/2) are tabulated in the sequence A215878 of the Online Encyclopedia of Integer Sequences.