'TimeWarp' CA rule -- anyone recognize this one?
Ilmari Karonen
program for my Amiga computer that allowed one to play with various CA
rules. (Actually, I had several of those, but I can't remember which
one I'm talking about in this post.)
One of the rules it featured was called TimeWarp. It was a 4-state rule
that would start much like an ordinary CCA, but after the grid was
covered in wavefronts so that just about all cells were oscillating with
period 4, the boundaries would gradually start to blur so that the waves
appeared to get longer and their speed proportionately higher, so that
it would look as if signals were propagating much faster than 1c. (Of
course, in fact the cells were mostly just oscillating in sync.)
That's just about all I remember. The rule seemed symmetric and was
presumably synchronous and using some smallish neighborhood. Oh, and
square lattice, of course. But I've no idea, for example, if it was
fully deterministic or not.
There's one more detail: the background image of my old web site at the
address http://www.sci.fi/~iltzu/gfx/bkgnd.gif is a screenshot of this
CA. You can see that it tiles nicely, because the rule was run on a
toroidal grid. I think one could even get the original state numbers
from the GIF palette, if one for whatever reason wanted to.
So, does anyone remember anything like this? I suppose I could always
try to find the original program and run it, but this has become a
somewhat nontrivial exercise by now.
--
Ilmari Karonen
If replying by e-mail, substitute .net for .invalid in address.
Ilmari Karonen
one like this, but I wanted to announce that I finally figured out the
rule I'd been looking for. I find it unlikely that anyone else would
care, but it's a personal triumph of persistence over lousy memory. :-)
On Wed, 08 Oct 2003 03:31:40 +0300, I wrote:
> One of the rules it featured was called TimeWarp. It was a 4-state rule
> that would start much like an ordinary CCA, but after the grid was
> covered in wavefronts so that just about all cells were oscillating with
> period 4, the boundaries would gradually start to blur so that the waves
> appeared to get longer and their speed proportionately higher, so that
> it would look as if signals were propagating much faster than 1c. (Of
> course, in fact the cells were mostly just oscillating in sync.)
To cut a long story short, it's not a CCA. It's the second-order
reversible outer totalistic rule b1234/s0123R on the von Neumann
neighborhood. (It turns out that there are quite a few second-order
rules on different neighborhoods that produce a similar effect.)
> There's one more detail: the background image of my old web site at the
> address http://www.sci.fi/~iltzu/gfx/bkgnd.gif is a screenshot of this
> CA. You can see that it tiles nicely, because the rule was run on a
> toroidal grid. I think one could even get the original state numbers
> from the GIF palette, if one for whatever reason wanted to.
I figured out the specific rule by visual comparison (in particular,
the Moore neighborhood tends to produce larger and less convoluted
domains) and finally by running the above-mentioned pattern backwards
under various rules until I found one where it evolves into a
low-entropy state.
In particular, if you run the MCell pattern below for 95 generations,
you should get the same result as in the GIF above. I say "should",
because I'm having trouble getting the pattern to load properly. This
is _probably_ because I'm running MCell with Wine under Linux, and the
emulation is sometimes less that perfect. Or it could be a bug in
MCell, I can't really tell.
If you use some other program, converting the pattern shouldn't be too
hard -- it's just a simple RLE format. So far, however, I've found it
surprisingly hard to find a program that would run this rule with the
appropriate geometry (256x256 torus) on a Linux/X system. If you know
any, pleasy do tell me.
(The rest of this message consists of the MCell pattern, 69 lines
long, described above. You can skip it if you're not interested.)
#MCell 4.00
#GAME Rules table
#RULE 2,0,1,
#RULE 0,1,1,1,1,0,0,0,0,0,3,3,3,3,2,0,0,0,0,0,
#RULE 1,0,0,0,0,0,0,0,0,0,2,2,2,2,3,0,0,0,0,0
#CCOLORS 4
#D TimeWarp rule, b1234/s0123R on the von Neumann neighborhood.
#BOARD 256x256
#WRAP 1
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--
Ilmari Karonen