A stochastic cellular automaton is a grid-based model that updates through random choices. In a coffee-mixing model, cells represent cream or coffee, and the starting grid separates them with a sharp boundary. section 8.1.1
Two update rules represent different assumptions about how particles move:
- In the interacting model, one adjacent cream–coffee pair is randomly chosen to swap places at each step. Particles cannot pass through one another, so mixing proceeds gradually. section 8.1.1
- In the noninteracting model, each cream particle independently jumps to a random adjacent cell. Particles can share a cell and do not block one another. section 8.1.1
To study large-scale patterns as the grid becomes microscopically random, the model’s state is smoothed into a coarse-grained array. Entropy is estimated separately from the fine-grained state using compressibility. section 8.1.1
Figure 8.2 Illustration of the construction of the coarse-grained array using an example grain size of 3. The values of the shaded cells on the left are averaged to produce the value of the shaded cell on the right. Used with permission granted by the lead author (Scott Aaronson).
The figure shows how averaging groups of cells produces a coarser array. section 8.1.1
