[seqfan] Re: PS re toothpick sequences - the movie version

[franktaw at netscape.net]

These are some of the cellular automata I was writing about in a 
previous post.  I first looked at these about 40 years ago.  Note that 
growing 1 neighbor on a hexagonal grid produces similar patterns.

I particularly like doing these on what I call an edge grid.  Take an 
underlying grid; the edge grid has one cell for each neighboring pair 
of cells in the original grid; these border when they share an 
underlying cell.  Basically, one makes each cell of the original grid a 
single point, and the cells are the lines connecting neighbors.  These 
often produce growth patterns similar to those on the underlying grid, 
but the pictures are nicer.

One particularly interesting automaton is on the edge grid for the 
Moore neighborhood (i.e., orthogonal and diagonal lines connecting the 
points of a lattice).  One draws an orthogonal line between two points 
where one has a single line into it and the other is empty; and a 
diagonal line where one has exactly two lines into it, and the other is 
empty.  (Also drawing a diagonal line between two points each with one 
line will not change the overall behavior.)  For quite some time, this 
appears to be growing in a perfect circle.  (The actual limiting shape 
is a not-quite-regular 16-gon.)

Franklin T. Adams-Watters


-----Original Message-----
From: Benoît Jubin <benoit.jubin at gmail.com>

I just tumbled upon this webpage:
http://www.santafe.edu/~moore/gallery.ht
ml
where in the section "cellular automata" are five nice pictures.  They
might be associated to other sequences however, given the rules.

Benoit