Rule 30 on Programmer.ie: Modern AI programming

Digital Life 03: The First Surprise

Tue, 11 Aug 2026 01:19:00 +0100

We ended the last chapter by changing one number.

rule = 22

became:

rule = 30

Nothing else changed.

Same world.

Same single active cell.

Same three-cell neighborhood.

Same synchronous update.

Same periodic boundary.

Same eight-bit lookup mechanism.

Only the rule changed.

And the spacetime diagram stopped looking simple.

There is visible structure on the left.

There is irregularity on the right.

There are repeating fragments.

There are regions that look almost patterned and then break apart.

Mon, 10 Aug 2026 18:23:00 +0100

Rule 30 is a perfect demonstration of why cellular automata are worth studying.

Its transition table contains eight bits:

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

Start from one active cell and repeatedly apply that rule.

The result rapidly stops looking like something generated by a tiny deterministic program.

Mon, 10 Aug 2026 18:22:00 +0100

An elementary cellular automaton has only three inputs per cell:

left centre right

Each input is one bit.

That means there are only eight possible neighborhoods:

111 110 101 100 011 010 001 000

For each neighborhood the rule chooses either 0 or 1.

Eight binary choices means:

2^8 = 256

possible rules.

The elegant part is that we can store one complete rule table in one byte.