[Пятничное] 10 Surprisingly Spectacular Simplest Cellular Automata
be careful, there are flashing gifs. They hidden under spoilersopen at your discretion. On a large screen, it is recommended to watch in a well-lit room.
traffic! (if it is still relevant in 2023)
Basic introductory
A cellular automaton is a model in which the state of cell-cells changes depending on the cells surrounding it. There are many characteristics of models, each of which has an even greater number of configuration rules.
The simplest representation of a 2D model includes the following characteristics:
cells have 2 states – alive / dead;
cells are squares without offsets;
the state change rules depend only on the number of living neighbors from the Moore neighborhood of the first order (8 neighbors);
the rules take into account 4 outcomes for each cell – birth, survival, death, emptiness.
This category of KA is called “Life-like”, after the name of the most famous machine with such characteristics – “Conway’s Game of Life”. Conway’s game of life runs on the rule B3/S23, i.e. birth cell (Birth) requires exactly 3 living neighbors, survival (Survival) 2 or 3 living neighbors. In all other cases, the cell dies (or remains empty).
On these characteristics, we have 218 rule options. Very few of them have received their own names in the community, beyond the usual notation naming. Today, let’s take a look at some interesting representatives.
0. Game “Life”
Out of the box, for a warm-up, let’s start with the classics. B3/S23
Due to the popularity of the machine, there are many named patterns/shapes. In this example, we see some of the simplest:
Steady (aka “still life”):
Resistant devourer “fishhook”
Periodic Flashers
Classic gliders or gliders
In random generation / development, it is difficult to catch more sophisticated patterns, but there are still many of them:
Absorbers and reflectors – structures that are not damaged by spacecraft colliding with them, destroying or reflecting them
And many others
The game “Life” has become a cult and has made a great contribution to the popularization of cellular automata. To this day, various possible configurations of objects are being discussed, and at interviews they can offer a simple task with iteration of this spacecraft.
1. Labyrinth
B3/S12345
Configuration with almost complete filling, without cell death.
On generations with a random start, patterns are found very rarely.
As with many KAs, starting state selection can produce some very impressive ornaments.
Labyrinths with modifications
B3/S1234 (without S5)
The Mazectric modification results in longer corridors, smoother and fuller spread, and more natural flashers.
B37/S12345 (with B7)
Labyrinth with “mice” flashing lights. An extra birth with 7 neighbors spawns mouse cells running around the maze, although they are limited only to straight corridors, colliding with each other.
And together – B37/S1234. Mazectric with mice.
It is interesting how the mice in this variant sometimes “lock” some freshly generated passages of the maze, becoming part of the latter.
2. H-trees
B1/S012345678
One of the most “predictable” KAs, not having any special patterns beyond its usual appearance. Therefore, it is more interesting to manually set the start with it, getting a certain final ornament.
3. Diameba
B35678/S5678
An engulfing rule with a number of well-known patterns.
4. Assimilation
B345/S4567
Another absorbing rule with a stable look. Strives for a rhombus, but does not always complete the figure.
The last generation shows that this rule also has oscillators – propellers, waves, arrows, beetles (I came up with the names myself ¯\_(ツ)_/¯).
5. Live free or die
B2/S0
Not the most spectacular, but conceptually interesting rule, referring to the American Revolutionary War motto (now the official motto of the state of New Hampshire) – cells survive only if they have no neighbors, but are born exclusively from two cells.
There is only one type of oscillator in the rule – duoplets (two cells located diagonally from each other), as well as several other figures, such as a gun and spaceships.
N. Seeds
A separate rule, but we will mention it outside the account, as a continuation of the idea of the past. Here is an even stricter survival condition – B2/S. That is, cells never survive, only new ones appear with two neighbors.
On this rule, the simplest spaceships are clearly visible.
6. Persian carpet
Let’s continue the idea of non-surviving cells. B234/S
Generation starting from a filled 2×2 block
Randomly distributed generation
There are several more interesting unnamed varieties of “carpets”:
B234678/S8
B2345678/S0238
B234567/S124567
B235678/S1234567
7. Corals
And end with spoilers. B3/S45678
A very slow but still growing rule with a lot of oscillators.
8. Coagulation
B378/S235678
Despite the apparent dynamism of the rule, cell aggregation occurs very slowly, with constant reverse outflows on the “shores”
9. Most
B45678/S5678
We are approaching completion, but we were only looking at the growing configurations. It’s worth fixing it.
A simple rule that collects cells into groups. All groups are oscillators in one form or another, and still lifes are impossible in principle.
10. Annealing
B4678/S35678
Another rule with a decreasing view, which comes to the final state only on the smallest still lifes and oscillators.
