Cellular Automata From First Principles 26: Cellular Automata as Computation

Mon, 10 Aug 2026 18:59:00 +0100

Cellular Automata From First Principles 26: Cellular Automata as Computation

A cellular automaton is a state machine distributed across space.

Each cell reads local information, applies the same transition rule, and writes a new state.

That is already a form of computation.

The deeper question is whether local patterns can carry, transform and combine information in a way that supports general computation.

Information needs carriers

In ordinary software, information lives in variables and memory addresses.

Cellular Automata From First Principles 04: Rule 110 and Computation in a Grid

Mon, 10 Aug 2026 18:24:00 +0100

Cellular Automata From First Principles 04: Rule 110 and Computation in a Grid

Rule 110 looks like another one-byte transition table.

111 110 101 100 011 010 001 000
 0   1   1   0   1   1   1   0

But its behavior gives us a much deeper idea: a cellular automaton can become a computational medium.

The important shift is this:

pattern generator
      ->
signal system
      ->
computation

Rule 110 is computationally universal. Matthew Cook published the universality proof in Complex Systems in 2004, showing that this elementary one-dimensional automaton can emulate universal computation.

Computation on Programmer.ie: Modern AI programming

Cellular Automata From First Principles 26: Cellular Automata as Computation

Cellular Automata From First Principles 26: Cellular Automata as Computation

Information needs carriers

Cellular Automata From First Principles 04: Rule 110 and Computation in a Grid

Cellular Automata From First Principles 04: Rule 110 and Computation in a Grid