I have been given a rule for a cellular automata (in which so long as one adjacent cell is living but not both the next generation lives), but I can't find any reference works on cellular automata rule numbers.
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You basically write out the 8 different conditions for the three cells to be in, and label each with a 0 or 1, based on whether the cell below them is alive or dead. The final string you get is interpreted as a number in base 2. There are nice graphical examples here – Joppy May 04 '17 at 13:30
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Ah! Thank you for explaining. – hamilton.julius May 04 '17 at 13:32
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How does the pattern for this rule get started ? If I am interpreting the rule correctly, a lone cell with no neighbours will die, so a single cell only lasts for one generation. – gandalf61 May 04 '17 at 14:29
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... unless dead cells come alive if they have exactly one living neighbour - in which case I think this is Rule 90 - see en.wikipedia.org/wiki/Rule_90. – gandalf61 May 04 '17 at 14:35
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Generate all three-bit numbers, of which there are 8. Each of those three bit numbers represents the three inputs to the automaton. The output of the automaton is a single bit. Interpret this sequence of output bits as a number.
For instance, rule 110 would indicate the binary number (note it is in LSB first) $0 1 1 1 0 1 1 0_2$ so we can say that $000_2\rightarrow0$, $001_2\rightarrow1$, etc.
law-of-fives
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