Gilbert tessellation

A Gilbert tessellation is a special pattern used in applied mathematics to understand how certain natural structures form. It helps explain patterns like mudcracks and needle-like crystals. This model was created by a mathematician named Edgar Gilbert, who studied it in 1967.

In this model, tiny cracks start forming at random points spread out like dots on a page. These points follow something called a Poisson distribution. From each point, a crack grows in two opposite directions along a straight line. The direction of that line is chosen completely at random. The cracks grow until they meet another crack, and when they do, they stop and form a T-shape.

The end result is a pattern that covers the whole plane with irregular shapes, called a tessellation. There is also a simpler version of this model where all the cracks can only grow sideways or up and down, making patterns of rectangles instead of more complex shapes. Scientists have found that real mudcrack patterns in nature often look very similar to what this model predicts.