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I wonder if you could create a fractal CA?
Imagine a CA, where each cell is actually 9 subcells. You apply the rules to
the subcells to make them live and dead. Then after each subcell generation,
you interpret those 9 cells to decide whether the supercell is alive or dead
(like, 5+ subcells alive means the supercell is alive or some such), and it
turns out the supercells are following the same rules as the subcells.
Just a curiousity triggered by earlier quantum-is-fractal link, Wolfram's
New Science ideas, Permutation City, and
http://alcor.concordia.ca/~vpetkov/Unreasonable%20Effectiveness%20of%20Mathematics.pdf
I wonder if there's a non-utterly-brute-force way of finding such a patter.
(First post was wrong group. :-)
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Yes.
Check out "A new kind of science" by Stephen Wolfram.
ian
"Darren New" <dne### [at] san rr com> wrote in message
news:49cbbde0$1@news.povray.org...
>I wonder if you could create a fractal CA?
>
> Imagine a CA, where each cell is actually 9 subcells. You apply the rules
> to the subcells to make them live and dead. Then after each subcell
> generation, you interpret those 9 cells to decide whether the supercell is
> alive or dead (like, 5+ subcells alive means the supercell is alive or
> some such), and it turns out the supercells are following the same rules
> as the subcells.
>
> Just a curiousity triggered by earlier quantum-is-fractal link, Wolfram's
> New Science ideas, Permutation City, and
>
http://alcor.concordia.ca/~vpetkov/Unreasonable%20Effectiveness%20of%20Mathematics.pdf
>
> I wonder if there's a non-utterly-brute-force way of finding such a
> patter.
>
> (First post was wrong group. :-)
> --
> Darren New, San Diego CA, USA (PST)
> There's no CD like OCD, there's no CD I knoooow!
>
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[GDS|Entropy] wrote:
> Check out "A new kind of science" by Stephen Wolfram.
I have, and I read the part before the reference text, but I don't remember
any discussion of how to improve the process of finding CAs with particular
rules. Indeed, I was under the impression that was one of the major points
he was trying to make.
Can you give me a hint less broad than "somewhere in a text roughly the size
of an unabridged dictionary"? :-) A chapter number, or topic name, or
something? Thanks!
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Darren New wrote:
> I wonder if you could create a fractal CA?
>
> Imagine a CA, where each cell is actually 9 subcells. You apply the
> rules to the subcells to make them live and dead. Then after each
> subcell generation, you interpret those 9 cells to decide whether the
> supercell is alive or dead (like, 5+ subcells alive means the supercell
> is alive or some such), and it turns out the supercells are following
> the same rules as the subcells.
Something very much like this has been done in the game of like
automata. It's called the "unit cell":
http://www.radicaleye.com/lifepage/patterns/unitcell/ucdesc.html
There's also a variant called the "deep cell" which allows you to
simultaneously simulate two independent versions of the game of life on
the same meta-grid. This lets you create a hierarchy of unit cells
while also being to simulate other patterns at each of the levels at the
same time.
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Kevin Wampler wrote:
> Something very much like this has been done in the game of like
> automata. It's called the "unit cell":
Very cool, thanks. I hadn't thought of using the turing completeness of it
to build a machine to calculate the rules. :-) That makes it much easier to
understand how it could be done.
That's a bit more contrived than I was hoping for, but it's a good start. :-)
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Darren New wrote:
> That's a bit more contrived than I was hoping for, but it's a good
> start. :-)
There is a more recent and even cooler (although equally contrived)
variation of this idea which uses streams of lightweight spaceships (ie.
horizontally/vertically moving glider-like patterns) to allow the
construction of "pixel" like patterns. You can then program these
pixels to simulate the game of life in a way which is visually very easy
to see:
http://b3s23life.blogspot.com/2006/09/brice-dues-game-of-life-metapixel.html
also for a better zoom-in:
http://b3s23life.blogspot.com/2007/04/hex-counter-and-cells-within-cells.html
http://otcametapixel.blogspot.com/2006/05/how-does-it-work.html
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Kevin Wampler wrote:
> There is a more recent and even cooler (although equally contrived)
> variation of this idea which uses streams of lightweight spaceships (ie.
> horizontally/vertically moving glider-like patterns) to allow the
> construction of "pixel" like patterns.
Very awesome! Thanks so much for the links and keywords. It's been years
since I seriously looked at anything conway.
If you like this sort of stuff, and you haven't read Permutation City,
http://www.amazon.com/Permutation-City-Greg-Egan/dp/006105481X/
I highly recommend it. One of my favorite novels.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Darren New wrote:
> If you like this sort of stuff, and you haven't read Permutation City,
> http://www.amazon.com/Permutation-City-Greg-Egan/dp/006105481X/
> I highly recommend it. One of my favorite novels.
I shall add it to my queue. Unfortunately the queue is a bit long at
the moment so it might be a bit before I can get around to it. Thanks
for the recommendation!
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