On a large m x n torus (or array), let p be the probability of land. When p is the inverse of the Golden Ratio, the expected number of islands (in black) and the expected number of pools (in blue) are equal, where:

On an island, we can move on black following North, South, East, and West.

In a pool, we can move on blue following North, South, East, West, NE, NW, SE, and SW.

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