Cool Universes in the Cosmos of
Cellular Automata
Readers familiar with the Game of
Life (see our main page; if not already
familiar, visit our introduction)
are probably aware of the existence of a number of
"otherworlds": cellular automata similar in nature(1)
to the Game of Life, but where the rules for when cells survive
or are born are different, resulting in patterns and structures
with very surprising appearances and behavior. The purpose of
this page is to present a number of such universes that seem to be extremely fascinating.
Due to the large amount of available information, rather than
putting everything in a single page, we prefer to devote
individual pages to each of those cool universes. Click on any of
the pictures, below, to move to the page where the corresponding
world is described. For another view at classification of
cellular atomata we encourage the reader to take a look at David
Eppstein's classification (see bottom of his page). However,
we follow our own empirical "classification" below,
because we are unable to characterize with certainty every case
presented here as belonging to one of Prof. Eppstein's four
classes.
"Otherworldly"
Cellular Automata
|
Expanding Universes
(most patterns
expand to infinity)
|
 Gems
Patterns smaller than around 12 x 12 become
oscillators of very high periods. Also, the slowest
glider resides here!
|
 Amoeba
Patterns have an aboeba-like appearance. Most patterns
larger than around 100 x 100 expand, but extremely
slowly; others vanish.
|
 A-maze-ing!
Most patterns explode fast with an aboeba-like border,
acquiring a texture with maze-like appearance.
|
 Coagulating
Blobs
Almost all patterns expand slowly in a circular-like
shape, creating coagulating blobs in the central region.
The blobs join and expand, containing inverse still lives
and oscillators.
|
 Corals
Rectangles filled randomly at a density of around 30%
produce blobs that first shrink fast, but then start
expanding slowly, resulting in coral-like or sponge-like
patterns.
|
|
Stable Universes
(most patterns
initially expand, then stabilize)
|
Stains
Patterns grow in unexpected directions,
until they stabilize to colorful oscillating stains.
|
|
|
Contracting Universes
(most patterns
contract, either disappearing, or becoming oscillators)
|
 Oscillators
Rule
Patterns shrink densely into tiny oscillators of
periods between 1 and 16.
|
 Spontaneous
Creation
Patterns shrink sparsely into oscillators, and a
puffer and a spaceship are almost always created.
|
 Spontaneous
Self-replication
Also known as "high life", this universe
often produces spontaneously a self replicating pattern.
|
Chaotic Universes
(most patterns
contract, but a few of them move or glide, disturbing the
debris and producing further action)
|
| |
|
|
Notes:
1.
Cellular automata such as Conway's Game of Life and all the
automata presented here belong to the class of totalistic
cellular automata, so called because in order to find whether a
cell will be born, survive, or die, we count its alive neighbors
and base our decision on the total sum of that counting.
Another possibility is to take into account the specific location
of some neightbors. (E.g., to state that a cell is born if its upper
and lower-left neighbors are simultaneously alive.) Still other
possibilities are to count more than the immediate eight neighbors, to allow
more than two states for each cell (i.e., alive and dead), to work in less or
more than two dimensions, to work with a non-orthogonal space (e.g., hexagonal),
and so on.
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