Living on a Random Torus

We don’t see doughnut shapes when we look up in the sky. But what if the Earth we live on were shaped like a torus instead of a sphere? This remote, but otherwise intriguing possibility, lead me to explore the formation of islands and pools in a toroidal world. In this exposition, I start with a programming perspective on counting islands and pools, and finish by presenting a probabilistic analysis of a random torus with a ratio p/q of land to water (p + q = 1). People on Earth have always been fascinated by the golden ratio φ = 1+ √ 5 2 . I presume the same would be true for the inhabitants of a torus. As it turns out, in counting islands and pools, the divine law of the skies