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Subject:
Cellular Automata and the Rule Fredkin
Category: Science > Math Asked by: kbarclay-ga List Price: $10.00 |
Posted:
16 Nov 2002 17:49 PST
Expires: 16 Dec 2002 17:49 PST Question ID: 109115 |
I am looking for references to a mathematical proof of Edward Fredkin's rule pertaining to Cellular Automata. This paper must have been published in the scientific literature, or done by reputable names (Wolfram, Langton, Fredkin himself). To satisfy my request I must be able to read this paper, and the proof must be clearly labeled and rigorous. By this rule, I am specifically asking for the rule describing self replication after a certain number of generations - the so-called "Parity Rule." This rule states that if the sum of the Von-Neumann neighbors is odd, the cell becomes alive. See http://cafaq.com/types/index.shtml#SECTION00011000000000000000 for a description of the rule. |
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There is no answer at this time. |
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Subject:
Re: Cellular Automata and the Rule Fredkin
From: mathtalk-ga on 16 Nov 2002 18:34 PST |
Hi, kbarclay-ga: According to Harold V. McIntosh, these are the published sources for Edward Fredkin's discoveries about replication under the "parity" rule: Martin Gardner, Wheels, Life, and Other Mathematical Amusements, W. H. Freeman and Company, New York, 1983. (ISBN 0-7167-1589-9 pbk) Brian Hayes, ``Computer Recreations - The cellular automaton offers a model of the world and a world unto itself,'' Scientific American, March 1984, pp. 10-16. A. K. Dewdney, The Armchair Universe, W. H. Freeman and Company, New York, 1988. (ISBN 0-7167-1939-8 pbk) http://delta.cs.cinvestav.mx/~mcintosh/newweb/ra/node2.html According to the same author, writing in this Cellular Automata FAQ: http://cafaq.com/properties/index.shtml "In turn, Fredkin has acquired widespread fame for the replication properties of the <exclusive or> when taken as a rule of evolution. However, it is difficult to encounter a single reference which can be cited, for either Toffoli or Fredkin, that can be fairly said to present their own views. Martin Gardner reported Fredkin's replication in his second article on Life in 1971, reprinted in [Gar83] thereby giving the idea worldwide publicity." I certainly consider Martin Gardner one of the "reputable names" in the literature of cellular automata, but since he doesn't appear on your short list, I will have to defer to your own judgement about his level of rigor, etc. regards, mathtalk-ga |
Subject:
Re: Cellular Automata and the Rule Fredkin
From: mathtalk-ga on 23 Nov 2002 14:54 PST |
Hi, kbarclay-ga: Since you mentioned Wolfram, I checked his recent book, Cellular Automata and Complexity, to see how he cites Fredkin's work (located from the index under "reversibility"), and found that while in the text he refers to a reference "Fredkin '82", in the actual list of references (at the end of that chapter) the entry becomes "E. Fredkin, 1981 (unpublished)" and a mention of a demonstration given at Three Rivers Computer Corp. -- mathtalk-ga |
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