Competitive Erosion

Sites start randomly red or blue. Random walkers alternate in color with reds starting at the top, blues at the bottom. Walks are constrained not to exit the disc, and stop when they reach a site of opposite color, changing it to their own color. This model was invented by Jim Propp.

1/2 blue
1/3 blue
1/4 blue
1/6 blue

Aggregation version with two sources. A red particle will stop when it reaches any non-red site (empty or blue) and turns that site red. The following were formed from 50000 particles of each color. As the sources get closer together, more particles get eroded and fewer aggregate.
sources at distance 200
sources at distance 50
distance 10
adjacent sources

Aggregation with twice as many reds released as blues:
40k red, 20k blue
80k red, 40k blue
160k red, 80k blue

320k red, 160k blue

Aggregation with a single source that alternately emits red and blue (to make things nontrivial, the source site itself has no color; walks just pass over it). These are five independent samples formed from 50 million particles of each color, nearly all of which annihilate each other:

(I'd like to check these on a different platform at some point, just to make sure the patterns are not some bizarre consequence of the random number generator!)

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