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The ⊔ trough function could perhaps be better named. Putting particles on top, falling into the abyss of NaNs on the side, seems more like a ⊓ table function, maybe? Not sure what the best name would be.

Maintaining a priority queue of "big" cells ( ≥ 4 ) might help the algorithm to focus on dispersal in the central cells, at least initially.

The ⊔ trough function could perhaps be better named. Putting particles on top, falling into the abyss of NaNs on the side, seems more like a ⊓ table function, maybe? Not sure what the best name would be.

EDIT

Yup, sure enough, if I deposit a quarter million particles on an otherwise zero surface of 100 x 100, using this code we see a 4 X speedup thanks to arithmetic.

 k = 12
 while np.nanmax(P) >= 4:
 for i, j in np.ndindex(sP):
 if P[i, j] >= 4 * k and not np.isnan(P[i, j]):
 P[i, j] -= 4 * k
 P[i + 1, j] += k
 P[i - 1, j] += k
 P[i, j + 1] += k
 P[i, j - 1] += k
 if P[i, j] >= 4 and not np.isnan(P[i, j]):
 P[i, j] -= 4
 P[i + 1, j] += 1 ...

The ⊔ trough function could perhaps be better named. Putting particles on top, falling into the abyss of NaNs on the side, seems more like a ⊓ table function, maybe? Not sure what the best name would be.