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Ladder

Cellular automata — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. rule 90: the eight neighbourhoods, read as the bits of 90and this is Pascal's triangle modulo two, checked cell by cell against the binomial coefficients

    Eight rules and a triangle

    A row of cells, each one deciding its next state from the three above it. Eight cases, one bit of output each — a rule that fits in a byte, and 256 of them in total. One of those bytes draws Pascal's triangle.

    rung 1 · dynamics
  2. rule 110: the eight neighbourhoods, read as the bits of 11060 rows from a random row

    The rule that computes

    One of the 256 elementary rules can run any program. Not simulate one, not approximate one — a machine that can compute anything computable, built from a lookup table with eight rows and nothing else.

    rung 2 · dynamics

All ladders