Ash
Dmitry Shintyakov
I am feeling interest to cellular ashes, i.e. random mix of stable and
cyclic patterns, resulting naturally from almost any random pattern,
big enough.
Despite it's stochastic nature, ash seems to have quite stable
properties. For example, the mean density of living cells in the (big
enough) ash in the Convay life is always near 0.027982, almost
regardless to initial density of pattern.
Ash seems simple object to research, but I haven't found much
information about it. Particularly, I am interested in:
* Mean ash density for different rules
* Density of specific simple patterns (blocks, blinkers etc),
especially for the Convay rules
* Other statistical properties of ash (here is one of my experiments:
http://dmishin.blogspot.com/2008/10/cellular-ashes.html)
* Reactions of ash with gliders.
* Stability of infinite large ash fields
Maybe, you can give me links or references to related materials?
Dave Greene
> information about it. Particularly, I am interested in:
> * Mean ash density for different rules
> * Density of specific simple patterns (blocks, blinkers etc),
> especially for the Convay rules
Have you seen Achim Flammenkamp's website?
http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html
http://wwwhomes.uni-bielefeld.de/achim/oscill.html
More recently, Andrzej Okrasinski's Life screensaver also generates
results you might find useful:
http://www.geocities.com/conwaylife/
(The second link is a huge PDF file containing object frequency data
-- though it looks like he's starting from relatively small fields of
random soup. Not sure if that will alter the statistics somehow.)
> * Other statistical properties of ash (here is one of my experiments:
> http://dmishin.blogspot.com/2008/10/cellular-ashes.html)
The Fourier transform image in your weblog entry was interesting. Are
you running the experiment on a torus, or does your final ash have
output gliders around the edges? If you do a Fourier transform of
your initial state (presumably a random soup of some kind) do you get
a similar square-symmetric pattern? My uneducated guess would be that
the algorithm is picking up on the strong regularity of the Life
universe grid -- take a look for example at the "seafan" image in
http://www.cs.unm.edu/~brayer/vision/fourier.html
which is a fairly regular arrangement of small cells, and has a
Fourier transform image reminiscent of your ash FT image.
> * Reactions of ash with gliders.
> * Stability of infinite large ash fields
Nick Gotts has done a lot of work in these general areas -- see for
example
http://nickgottsgol.blogspot.com/
-- but he focuses on "sparse" initial conditions rather than normal-
density random ash fields.
Seems to me that infinite ash fields are going to be stable *unless*
it's possible to build a replicator with an ash-cleaning attachment
that works really, really well -- obviously it would have to be able
to clean out more than one replicator's worth of ash-infested space,
on average, before hitting something it couldn't handle and blowing
up. And a replicator-plus-ash-cleaner is likely to be much larger
than a plain-vanilla universal-constructor replicator that works in
nice safe empty space.
A reliable ash cleaner seems very unlikely to exist based on my
experience so far... but an infinite Life grid has every possible
finite configuration in it somewhere, with probability 1 (right?) so
experience isn't necessarily a very good guide here.
With enough hand-waving, I could "design" an ash vacuum-cleaner that
would carefully reach out from behind a screen of shielding blocks and
test nearby space, one cell at a time, with a (purely hypothetical)
reaction that cleanly annihilated most common objects. Annihilation
reactions are easy enough when you know what you're cleaning up and
exactly where it is, but something that works even for all phases of
blinkers *and* all orientations of boats, blocks, and beehives is a
matter of wild speculation. It would probably take years of effort
and a good source of funding, at least, to get past this hand-waving
theoretical stage...
But it does seem vaguely within the realm of possibility. The
reaction would have to send back an "all clear" signal each time the
test reaction occurred without a hitch -- meaning the tested cell was
blank. And it would patiently restart the whole cleaning process from
Cell 1 whenever the "all clear" signal didn't come back: in that case
the cleaner must have run into something it couldn't handle, and that
means there's now an unknown amount of new ash to clean up... plus the
glider-absorbing shield may need repair (!).
Probably even if it didn't fail catastrophically, any design like this
would get stuck in an infinite loop pretty quick, upon hitting its
first "cleaner-proof" ash -- an eater pattern that happens to absorb
the test reaction without itself being altered. But an advanced
universal constructor would be perfectly capable of monitoring its
cleaning attempts and trying an alternate test reaction if the first
one repeatedly fails to work.
Add enough clever tricks and failsafe devices, and just possibly
there's something out there with a better-than-even chance of actually
copying itself into an ash field. Clearly such a replicator won't get
through a full cleaning cycle in any reasonable amount of time. But
it still might end up dominating an infinite Life grid -- given all
the time in the Universe.
Keep the cheer,
Dave Greene