3D automata with Life-style objects
Thomas Womack
the latter sort - state at time t+1 depends on state at time t and
count of neighbours) which exhibits the same sort of behaviour as Life
(that is, a reasonable range of naturally-occuring still lives and
short-period oscillators)?
Gliders seem to exist in a number of 2D totalistic and semi-totalistic
automata; are any known in 3D models, or in exotic neighbourhoods (eg
hexagonal grids in 2-space, octahedral grids in 3-space)?
Tom
mayd...@bayarea.net
Thomas Womack <mert...@sable.ox.ac.uk> wrote:
> Gliders seem to exist in a number of 2D totalistic and semi-totalistic
> automata; are any known in 3D models, or in exotic neighbourhoods (eg
> hexagonal grids in 2-space, octahedral grids in 3-space)?
Apparently I have been at least moderately successful at discovering
(engineering?) many hexagonal grid cellular automata with gliders. I
use two different twelve neighbor neighborhoods for my most interesting
hexagonal CA's, which I call the star and asterisk neighborhoods. I
also cheat by using refractory states a la Brian's Brain, a CA in which
all structure is dynamic and gliderlike.
On my web page at www.bayarea.net/~maydwell/ca you can find models
which implement hexagonal CA's with different neighborhoods, including
six and eighteen neighbor rule examples. Inside the source code for the
hex star and hex asterisk models is an English description of each
rule. If you are using Windows you can run these models on SARCASim, my
fast programmable CA simulator.
Dimensionality is truly an illusion on a machine with linear addressing
space: any one dimensional CA simulator which allows arbitrary neighbor
specification and provides support for protective border cells can be
used to simulate an N-dimensional grid CA of fixed size. SARCASim, at
heart a one dimensional CA simulator with symbolic names for row
offsets, is capable of doing this. Assume one wants to simulate a 2x2x2
cube, not counting border cells. In ARCAL, SARCASim's rule
specification language, neighbors are specified by compass point
abbreviations, which can be catenated. So given the fixed dimensions
above and accounting for borders the offsets to the directly
neighboring plane cells may be specified as NNN or SSS.
Here is what the resulting two dimensional board will look like.
Numbers indicate the plane number of each cell the plane, while B's
represent the border cells needed to separate planes:
1 1
1 1
B B
2 2
2 2
Using the current version of SARCASim to set up and simulate three
dimensional CA one should be able to discover (engineer?) interesting
fast three dimensional CA rule specifications which spawn gliders
quickly traversing mostly empty "universes". My opinion is that the
interesting three dimensional CA's you want are out there, just waiting
to be discovered and named.
Enjoy,
George Maydwell
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