Crystal Domains
16 states, threshold 3, range 2 — a wider view and a high bar
A wider neighbourhood and a high threshold slow everything down, so flat crystal-like regions form and their borders grind against each other.
How it works
In plain English, before the notation
This rule looks two cells out in every direction, so each cell sees 24 neighbours instead of 8, and it needs three of them in the next state before it will change. The wide neighbourhood averages out local noise and the high threshold makes change expensive, so the grid settles quickly into large flat regions that then spend a long time grinding against each other along their borders.
Watch domains form and then compete
- Open Presets and load "Crystal Domains" and press Play.
- Large regions of a single colour appear within the first hundred steps.
- After that, watch only the borders. The interiors are effectively frozen; all the activity is at the seams.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
Well-known rules
Where it came from
Range and threshold are the two parameters that most change the character of a cyclic rule. This configuration sits at the high end of both, and demonstrates the regime that Fisch, Gravner and Griffeath described as producing large, slow-moving domains rather than waves.
The rule, precisely
What each cell looks at
24 neighbours at range 2 (a 5×5 block, excluding the centre)
What a cell can be
States 0 to 15, arranged in a cycle
The update
next = (k + 1) mod 16 if at least 3 of the 24 neighbours are in state (k + 1) mod 16; otherwise k
16 states, threshold 3, range 2. The range is what changes the neighbourhood from 8 cells to 24, and it is the most expensive parameter to increase — the work per step grows with the square of the range.
Large domains, slow borders
The wide neighbourhood suppresses fine detail entirely:
- Uniform regions appear quickly and become large, because the wide neighbourhood smooths over local variation.
- Domain interiors stop changing; all remaining activity is confined to the boundaries.
- Boundaries move slowly and irregularly, and larger domains tend to absorb smaller ones over time.
- With 16 states the full cycle is long, so a given region holds its colour for a while before advancing.
Not applicable
Studied for its coarsening behaviour, not for computation.
Grain growth in metals
When a metal cools, it forms crystalline grains that then grow at each other’s expense — large grains absorb small ones, and all the action is at the grain boundaries. The geometry here is the same, arrived at from very different rules.
Things to try
- This rule is heavier than the others: the 5×5 neighbourhood means about three times the work per cell. Increase Cell Scale if the frame rate drops.
- Paint a small region of one colour deep inside a large domain and watch how long it survives.
- Leave it running for several thousand steps — the coarsening is slow and is the interesting part.