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] sanrrcom> 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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