- #1
EebamXela
- 16
- 0
I was messing around with cellular automata and wanted to test a theory i had.
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
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