We can see lots of patterns in nature: leopard spots, butterfly wing eyes and zebra stripes to name a few. While these all look pretty different, it turns out that there is a simple set of mathematical rules that can produce all these patterns. Alan Turing (the guy who created these rules) thought of cells as producing 2 chemicals that act very differently to each other. The rules show us that one of these chemicals spreads out faster than the other, leading to the slower chemicals all getting trapped in clumps. These clumps can be in different shapes like spots and stripes.
Knowing how these patterns are made is important for something called tissue engineering. This is because we can get cells outside of the body to organise themselves in the way they do naturally. These are then used to create tissues to replace damaged tissue eg. artificial skin for people with bad burns.