User:TheWayOfTheCon/Specific properties of cellular automata
I believe that cellular automata can be described in more ways than "Stable, chaotic, or explosive". There seems to be more nuance and complexity to how certain rules evolve and take shape, that just needs to be described and defined. In general, I believe that there is more predictability and distinguishable properties in cellular automata than we think. And so, in this user article, I will showcase several different indices and measurements I have come up with in the hopes that these can be used to better describe a rule and its characteristics.
I will note that:
- These properties are intended use on for two-state Moore neighborhood rules
- Some of the properties trying to be evaluated here might not be the most useful, and I'm totally open for feedback, although no one property should be used to fully describe a rule
Entropy
Entropy is the average time large soups take to stabilize. It can be used to figure out how quickly (or slowly) patterns will take to die off.
Small pattern potential
Small pattern potential (SPP) is a property meant to gauge how much small patterns in a rule are to grow in population during their evolution, by comparing the initial and maximum populations. Tetraplets are to be used specifically.
To calculate a rule's SPP, take a tetraplet and divide its maximum population by its initial population (always 4). Repeat the process for all 22 possible tetraplets and find the average. By definition, the lowest SPP a rule can have is one, where no tetraplets evolve to have more than four cells.
| All 22 tetraplets. Life has an SPP value of 1.52273. (click above to open LifeViewer) |
| Rule name | Rulestring | SPP |
|---|---|---|
| Conway's Game of Life | B3/S23 | 1.52273 |
| LowLife | B3/S13 | 1.19318 |
| Day & Night | ||
| 3-4 Life | ||
| Snowflakes |