3D Cellular Automata
Marius Ibenhart Watz
Hello. I am a computer artist working with 3D rendering
and animation as a creative means of expression. I've
been interested in Alife for a while now, and lately
I've been thinking of simulating CA in three dimensions
as well as animating them. I'm especially interested
in automata similar to the Game of Life, but in 3D.
Has any work on this shown stable configurations like
ships, gliders and guns in 3D CA? If so, where may I
find references.
Also, it strikes me as strange that noone has suggested
using a spherical grid to simulate CA growth on. Such
a grid would wrap-around properly, and it would enhance
visualization.
--
Marius
NEW EMAIL ADDRESS: m.i....@usit.uio.no
http://www.uio.no/~mwatz/
Michael Wade Snyder
>
> Hello. I am a computer artist working with 3D rendering
> and animation as a creative means of expression. I've
> been interested in Alife for a while now, and lately
> I've been thinking of simulating CA in three dimensions
> as well as animating them. I'm especially interested
> in automata similar to the Game of Life, but in 3D.
> Has any work on this shown stable configurations like
> ships, gliders and guns in 3D CA? If so, where may I
> find references.
>
> Also, it strikes me as strange that noone has suggested
> using a spherical grid to simulate CA growth on. Such
> a grid would wrap-around properly, and it would enhance
> visualization.
People have- it isn't basically putting the game of
life on a planet- but it doesn't change the operation much- all
you do is provide the equivalent of a wrap around screen- the
screen is arbitrary to begin with. In 2-D it doesn't look any
more impressive except shapes at the edges have halves at
opposite ends of the screen- in 3-D representation, you can't
see all the grid at once. Though it is kinda cool anyway.
Kimmo K K Fredriksson
..
: as well as animating them. I'm especially interested
: in automata similar to the Game of Life, but in 3D.
: Has any work on this shown stable configurations like
: ships, gliders and guns in 3D CA? If so, where may I
: find references.
Yes, there are several Game of Life in 3D implementations, you might
check the life.anu.edu.au (hope I got this correct), for example.
: Also, it strikes me as strange that noone has suggested
: using a spherical grid to simulate CA growth on. Such
: a grid would wrap-around properly, and it would enhance
: visualization.
CAs aren't usually intended to make nice visual effects...
: --
: Marius
: NEW EMAIL ADDRESS: m.i....@usit.uio.no
: http://www.uio.no/~mwatz/
--
/\ /\ /\/\/\/\ Kimmo.Fr...@Helsinki.FI
/\ /\ /\
/\ /\ /\ Kimmo Fredriksson []
/\/\ /\/\/\ Porvoonkatu 14 A 15 [] []
/\ /\ /\ 00510 Helsinki [][][] [][]
/\ /\ /\ FINLAND [] []
Richard Ottolini
around 1989-1990 discusses the topic and gives a few interesting
rule sets. I remember coding a displayer on an Ardent at that
time to view such.
David Ardell
> : using a spherical grid to simulate CA growth on. Such
> : a grid would wrap-around properly, and it would enhance
> : visualization.
>
(Fall-Winter, 1992; 7:2). It shows a spherical CA entitled "Global CA" in
which emergent species compete for grid-space. The cover is in color, and
different species occupy domains displayed in different colors -- it looks
like nation-forming.
It's creator is Ron Hightower, an ex-student of Stephanie Forrest's, who
used a GA to "evolve competitive components of the immune system"
(according to the write-up).
*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*
David Ardell
Department of Biological Sciences
Stanford University
David Q. Spitzley
don't know how much work has been done with CAs in triangularly tiled
matricies.
Wayne Tvedt
There was a series of papers by Carter Bays in the first
few volumes of the journal _Complex Systems_, ca. 1987-1992.
These are all cited in the CA FAQ,
http://www.santafe.edu/~hag/ca-faq/ca-faq.html
Bays looked at several spots in the paramerization space
of 'semi-totalistic' ('semi-totalistic' that my new state
is a function of only my own state and the sum of my neighbors'
states) on cubic as well as 'half-cubic' lattices. (by 'half-
cubic' I mean a certain spherical packing which is equivalent
to a checkered cubic lattice where the cubes/spheres connect
only along the cubic edges.)
: Also, it strikes me as strange that noone has suggested
: using a spherical grid to simulate CA growth on. Such
: a grid would wrap-around properly, and it would enhance
: visualization.
what do you mean by 'properly'? One of the main constraints
for CA is isotropy, and you can't do a spherical tiling (with
regular polygons) without it being either very small (eg, an
icosahedron) or having exceptional points, which might have
vortex-like effects on the global scale. Most CAists seem
content to use toroidal wrap-around, ie, matching opposite
sides of a square lattice, which visualizes just fine (don't
even need 3-D.) But maybe you could generalize the concept of
CA to include irregular tilings which are _stastically_
isotropic, and find an irregular tiling of the sphere to do
travelling waves on. (And I think it would be _cognitively_
easier to visualize patterns moving on the sphere than it
would be on a torus, even though you couldn't show the whole
sphere without distortion, just because most of us have more
tactile experience with spheres than with torii.) Also, I would
think that glider patterns which are stastically stable on
irregular lattices would be much more interesting than those
on regular lattices.
Wayne Tvedt
Andy Duncan
> Also, it strikes me as strange that noone has suggested
> using a spherical grid to simulate CA growth on. Such
> a grid would wrap-around properly, and it would enhance
> visualization.
Well, you can't map a rectangular grid onto a sphere. If you assume the
left and right edges of a rectangular Life board are connected, and likewise
the top and bottom edges, you get a torus. I wrote a Mac program that
used toroidal topology with Life and let you resize the window. Interesting
things happen in small toroidal spaces.
If you let there be a half twist (orientation reversal) across one of the
connections between edges, you get a Klein bottle. My program also addresses
this possibility; things get even stranger. Scrolling is not well-defined
in one direction.
Andrew Duncan
Philips Interactive Media
adu...@aimla.com