[seqfan] Re: Toothpicks in Z^n.

franktaw at netscape.net franktaw at netscape.net
Fri Nov 22 12:36:26 CET 2013

The toothpick sequences are just one special case of a class of growing 
automata. The most fundamental example of these is the rule that any 
cell with exactly one neighbor on turns on, and once on it stays on. 
This latter rule works for essentially any space.

While the toothpick sequences are very nice, I think people ought to 
look at the simpler cases first.

Franklin T. Adams-Watters

-----Original Message-----
From: L. Edson Jeffery <lejeffery2 at gmail.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Fri, Nov 22, 2013 5:24 am
Subject: [seqfan] Toothpicks in Z^n.

Are there any known generalizations of any the (very nice) toothpick
sequences by Omar E. Pol to higher dimensions? I have searched and found
nothing so far. For example, for the T-toothpicks 
it seems possible to construct some kind of analogue in Z^n (Z is the
integers), for n>2, perhaps without much modification to the rules for 
planar case.

Cf. http://oeis.org/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS

Ed Jeffery


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