From: mcintosh@uapnx1.dgsca.unam.mx (Harold V. McIntosh)
Subject: Random automata, 3-D automata.
X-Unparsable-Date: Mon, 6 Apr 92 10: 10:20 MEX
Organization: The Internet
Distribution: inet
Date: Mon, 6 Apr 1992 16:14:18 GMT

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Bill Tozier/Vaguery <bill@AMY.MED.UPENN.EDU> (Fri, 27 Mar 1992 10:03:37  
EST) inquires, among other things:

> Has anyone examined CA on (fixed) random graphs, rather that regular
>   tilings?

There must be numerous references for this. Try: [Stuart A. Kauffman,  
Emergent properties in random complex automata, Physica 10D 145-156  
(1984)]. Random graphs have marvellous properties; he alludes to some of  
them. 


Try also: [Max Garzon, Cellular automata and discrete neural networks,  
Physica D45 431-440 (1990)] and: [C.C. Walker, Attractor dominance  
petterns in sparsely connected boolean nets, Physica D45 441-451 (1990)].  
Both articles come from an issue of Physica D that was a conference  
proceeding, edited by Howard Gutowitz, now reprinted by the 

MIT Press.

These references are the tip of an iceberg; each contains further  
references and constitute backwards pointers for Science Citation Index.
 

>  Is there any class of CA in which cells "drop out" of the array? By
>    this, I mean that a cell not only arrives at a fixed state, but *if
>    its state is changed at random* it will not affect the dynamics of
>    the remaining array? (I can see the trivial case in which the number
>    of neighbors is zero for all cells, but I mean something a bit more
>    than that...:-))

Just add an additional bit to the state set signifying that the cell has  
"dropped out" and modify the evolutionary rule accordingly. You can even  
concoct situations in which the cell "drops back in." Although it would  
complicate the rule set horrendously, you could use the same technique to  
change rules, make them evolve, and so on. The real 

problem lies in setting up some reasonable context in which you would want  
to do such things.

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Jon McCormack <jonmc@BRUCE.CS.MONASH.OZ.AU> (Fri, 27 Mar 1992 20:10:24  
GMT) says:

>  I'm interested in computer graphics application using CA and I
>    was wondering if anyone could point me in the direction of some
>    references to 3D CAs. I recall seeing some animation of what
>    looked like a 3D version of a lattice gas simulation. It was
>    a bubling surface, I presume a volumetric CA converted to a
>    surface representation.

The name often associated with 3-D automata is Carter Bays, who has  
published in Complex Systems over the years, and was featured in A.K.  
Dewdney's "Computer Recreations" column in Scientific American. The  
specific issue, cover adorned by a 3-D automaton, was February, 1987;  
three of his Complex Systems articles appeared the same year.

The October, 1991, issue of Dewdney's magazine "Algorithm" has an article  
on electronic Lava Lamps by Clifford A. Pickover; it is likely that he has  
published in other places, such as the IBM Systems Journal. One should  
look him up in Citation Index. The Lamp is a 3-D automaton running a sort  
of majority rule.

Recreationally, 3-D automata suffer from being hard to visualize, not to  
mention a dearth of really "interesting" automata. Scientifically, they  
aren't much better off, but perhaps there are persons who can provide us  
some further information about them.

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Harold V. McIntosh		|Depto. de Aplicacion de Microcomputadoras
mcintosh@uapnx1.dgsca.unam.mx	|Inst. de Ciencias, UAP, Apdo. Postal 461
MCINTOSH@UNAMVM1  (BITNET)	|72000 Puebla, Pue., Mexico
Newsgroups: comp.theory