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If you look close at the elementary cellular automata Rule 30 you'll notice that the right

side is chaotic, while the left side has chaotic properties but it does have order and

repetition.

There is an imaginary line that you could draw that separates the two sides that slopes

slightly to the left.

My theory was that the ratio of the right side and the left side of each row follows closely to

the Golden Ratio.

I've attached an image of the first 10,000 iterations of Rule 30 and overlaid a red line that

represents the golden ratio dividing line (not the actual dividing line). You should see that

for a while up at the top the golden ratio line and the actual separation point match up

almost perfectly. But eventually they start to separate.

Is this just a coincidence? Or is there something to this?

1000 Iterations

10,000 Iterations