[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
(https://oeis.org/A160172),
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
the
planar case.
Cf. http://oeis.org/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS
Ed Jeffery
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