A "new" Conway Life experience.
Toon Moene
I'm a physicist, not a numerical combinatorialist (if that's a word).
I was playing with xlife, while waiting for a compile of our weather
forecasting model, and came up with the following, interesting, combination:
Rules: 23/37 (i.e., life continues with 2 or 3 neighbours and starts
with 3 or 7 neighbours).
and the following starting pattern:
X XX
X X
XX X
It creates an (initially) rapidly expanding universe (that I called "The
Big Bang" tentatively), that never fills completely up.
I thought the following questions would be interesting:
1. Does this universe expand forever ?
2. If yes, what is its rate of expansion ?
3. What is its ultimate density ?
I - perhaps foolishly - incorporated these questions into the Wikipedia
entry of Conway's automata, and got thrown out within ours. So perhaps
this *is* not encyclopedian knowledge, but something to reason about.
Thanks,
--
Toon Moene - e-mail: to...@moene.indiv.nluug.nl - phone: +31 346 214290
Saturnushof 14, 3738 XG Maartensdijk, The Netherlands
At home: http://moene.indiv.nluug.nl/~toon/
Who's working on GNU Fortran:
http://gcc.gnu.org/ml/gcc/2007-01/msg00059.html
Kent Paul Dolan
> L.S.,
> I'm a physicist, not a numerical combinatorialist
> (if that's a word).
> I was playing with xlife, while waiting for a
> compile of our weather forecasting model, and came
> up with the following, interesting, combination:
> Rules: 23/37 (i.e., life continues with 2 or 3
> neighbours and starts with 3 or 7 neighbours).
> and the following starting pattern:
> X XX
> X X
> XX X
> It creates an (initially) rapidly expanding
> universe (that I called "The Big Bang"
> tentatively), that never fills completely up.
> I thought the following questions would be interesting:
> 1. Does this universe expand forever ?
Since it spews gliders to the four diagonals,
of necessity, the answer to that is "yes". "Yes"
also looks to be the correct answer for the central
blob, which begins starfish shaped but rapidly
becomes fairly disk shaped.
> 2. If yes, what is its rate of expansion ?
Golly can show you that, it counts both population
and generations. Overall, though, since it spews
gliders, it expands at C/4.
> 3. What is its ultimate density ?
Probably asymptotically zero; the body of the blob
grows lots slower than the tips of the arms
separate, so the area of the total population
between X bounds and Y bounds becomes a smaller and
smaller fraction of the number of cells within those
bounds.
> I - perhaps foolishly - incorporated these
> questions into the Wikipedia entry of Conway's
> automata, and got thrown out within ours. So
> perhaps this *is* not encyclopedian knowledge, but
> something to reason about.
> Thanks,
> Toon Moene - e-mail: t...@moene.indiv.nluug.nl - phone: +31 346 214290
> Saturnushof 14, 3738 XG Maartensdijk, The Netherlands
> At home:http://moene.indiv.nluug.nl/~toon/
> Who's working on GNU Fortran:http://gcc.gnu.org/ml/gcc/2007-01/msg00059.html
Toon,
That is indeed a very fertile rule and seed.
In Golly, that rule reads backwards to the way you
gave it, B37/S23, by the way.
I stuck the rule and seed into Golly, and after a
few tens of thousands of generations, stuck another
seed in such that the arms of gliders spewed by the
two blobs would intersect, and without any more
planning than that, it constructed a puffer train,
that survived ten or twelve major pattern
replications despite the sleet of gliders colliding
with it, before it finally got clobbered hard enough
to disrupt its progress. By then the two major blobs
had merged; whether they could do that was one of
the things I was trying to learn.
Another thing I learned is that it is somewhat
difficult to get a survinging population from a
random start. Doing that took me a couple of tries
after I nerfed the first experiment.
Golly lets you back far away from the pattern, and
see it in the large, and the one your seed creates
is quite beautiful from a distance. The one from a
random start is almost as pretty, but not so
symmetrical.
I suspect you have satisfied the earlier request
here for a more fertile and interesting rule than
Conway's original. Was that request from you? I've
forgotten.
xanthian.
Toon Moene
> Rules: 23/37 (i.e., life continues with 2 or 3 neighbours and starts
> with 3 or 7 neighbours).
>
> and the following starting pattern:
>
> X XX
> X X
> XX X
>
> It creates an (initially) rapidly expanding universe (that I called "The
> Big Bang" tentatively), that never fills completely up.
Duh, bad reproduction of pattern. It should be:
X
XX
X X
XX
X
--