# Moore neighborhood on a two-dimensional Cartesian lattice

How many distinct cellular automata rules are there that use the Moore neighborhood on a two-dimensional Cartesian lattice if we allow three bits (eight states) per site?

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If you wish to ask a similar question changing the lattice to three dimensions and two bits per site, append the question or ask a new question. Please don't alter the question so that the existing answers make no sense. –  robjohn Feb 9 '13 at 15:42
Please do not deface the question. It orphans the answers that people have given. –  robjohn Feb 11 '13 at 18:36

A rule is a function from the input space (here of size $8^8$) to the output space (which is of size $8$). There's $(8^8)^8 = 2^{24 \cdot 8} = 2^{192}$ such functions.