Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

ONT Cactus Rules


o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

CR.  Note 1

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

With an eye toward the aims of the NKS Forum, I've begun to work out
a translation of the "elementary cellular automaton rules" (ECAR's),
in effect, just the boolean functions of abstract type q : B^3 -> B,
into cactus language, and I'll post a selection of my working notes
here.  By way of the briefest possible reminder, this cactus syntax,
in its existential interpretation and its traverse-string redaction,
uses just two series of k-adic connectives, first, the concatenation
of k expressions is read as their k-adic logical conjunction, second,
a bracket of the form (e_1, ..., e_k) is read to say that exactly one
of the k expressions e_1, ..., e_k is false.  I may sometimes refer to
this bracket as a k-adic "boundary operator" or a k-place "cactus lobe".

Reference Material:

http://atlas.wolfram.com/
http://atlas.wolfram.com/01/01/
http://atlas.wolfram.com/01/01/views/3/TableView.html
http://atlas.wolfram.com/01/01/views/172/TableView.html

Incidental Musement:

http://www.pinball.com/games/cactus/

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o