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Ask HN: Why multiples of 512 of the Cellular Automata panels show dark canvases?

4 points by jdironman ↗ HN
Why do multiples of '512' using the Wolfram alpha Automata panels show dark gray canvases?

(For example, 512,1024,2048, etc...)

https://www.wolframcloud.com/objects/sw-blog/capanels

2 comments

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db48x
It's not blank, it's just that there are no cells to turn yellow.

These panels are fairly small rectangles clipped out of a larger plane, so it could be that there are filled cells elsewhere that don't show up here.

However, if you think about how the number 512 looks in binary (2#1000000000) you can see why the rule would make for a lot of blankness. Only one bit is set, and that bit corresponds to a pattern that doesn't occur in the initial conditions used by this page, which has only one cell filled in. If you ran this rule with different initial conditions, you would get a different image.

Also note that you're looking at rules which are powers of two, not just multiples of 512. (For example, rule 1532 is not entirely blank).

jdironman
Just as 1532 is not, 384 and 768 isn't blank either. I was racking my brain trying to find a pattern and was really just unsure what it was that I was looking at here.Thank you very much for your informative answer. I figured that it had deeper relation on a binary level of things. I plan on reading more into this as it is fascinating.