11–20 of 52 posts
Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone figured it out.
What are the implications of positive/negative answers to these questions, and/or what else aside from "because it's there" motivates answering these questions?
Who knows? Answers to these questions might spur discussion on connections between cellular automata and other computational constructions. I think that's Wolfram's angle -- justify the cellular-automata-is-everything tack that he's been on the past 20-30 years.
https://www.kickstarter.com/projects/fbz/knityak-custom-math...
They make great tattoos too:
http://i.imgur.com/mct1AFX.jpg
https://geekytattoos.wordpress.com/2011/04/14/wolfram-2-stat...
That one is actually quite controversial:
https://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_T...
I gave some links to visualizations of CA basins of attraction including Rule 30 in my previous post about "Garden of Eden" configurations: https://news.ycombinator.com/item?id=14468707 There's a thing called a "Garden of Eden" configuration that has no predecessors, which is impossible to get to from any other possible state. For a rule like Life, there are many possible configurations that must have been created by…
The PDF is here: http://users.sussex.ac.uk/~andywu/downloads/papers/global_dy...
I gave some links to visualizations of CA basins of attraction including Rule 30 in my previous post about "Garden of Eden" configurations: https://news.ycombinator.com/item?id=14468707 There's a thing called a "Garden of Eden" configuration that has no predecessors, which is impossible to get to from any other possible state. For a rule like Life, there are many possible configurations that must have been created by…
The third link is a dead link, but it looks like it's up here now: http://users.sussex.ac.uk/~andywu/gdca.html The PDF is here: http://users.sussex.ac.uk/~andywu/downloads/papers/global_dy...
love this phrase: "naturally constructed" numbers, suggesting that the numbers we use every day are themselves computational conveniences, and possibly that another number construction could be useful at other scales.
It is pretty hard in general to prove that calculating things takes at least O(n) time, so I wouldn't expect that one to be solved any time soon. Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone fi…
It's much simpler depending on the answer to the first question, right?
It's been a while since I've touched big-O, but I'm pretty sure that if the center column is periodic (period of P cells), then it follows that you just have to compute the P cells and then index into them, which makes it O(1).
This doesn't appear to be true for arbitrarily many digits, and I'm struggling to see how the two fields may even be connected. Some properties appear similar, eg. the Möbius function, too, appears to sum up to 0.
It is pretty hard in general to prove that calculating things takes at least O(n) time, so I wouldn't expect that one to be solved any time soon. Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone fi…
Have you seen the Miller-Fredkin paper on circular motion of strings in cellular automata?
Has anyone seen a version of Rule 30 for a 2D array, instead of 1D? I'm doing some searching but can't find one. Somewhat tangential to my angle of attack, but would be helpful to me.
EDIT: Oh I understand now! Each generation is 1D. Thanks for explaining! :D
