Gilbert tessellation

A Gilbert tessellation is a special pattern used in applied mathematics to help us understand how some natural shapes form. It can explain patterns like mudcracks and needle-like crystals. This idea was created by a mathematician named Edgar Gilbert in 1967.

In this pattern, tiny cracks start 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 the line is chosen at random. The cracks grow until they meet another crack, and then they stop and form a T-shape.

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