Many fish have patterns on their skin that are made up of tiny cells of different colors, including black and yellow. Patterns form because the cells follow specific rules. Figuring out these rules is important in biology. Mathematicians help discover these rules by simulating pattern formation -- like growing a fish pattern on your computer! You can try it yourself on this website and read more about it here.


Step 1: To build a pattern with math and computer coding, first choose a starting point (what your fish looks like when it's young, before its full pattern forms):

Step 2: Fish develop different patterns when the cells in their skin follow different rules for how to act. Pick a rule from the options below:

Now you are ready to simulate pattern formation with a mathematical model -- hit start!

You can press pause or click reset to start over. Try picking different starting points and rules to explore all the patterns that you can create.

Simulated Pattern Formation

Simulation Settings

To control how fast cells appear in the pattern, select a simulation speed below:

Select a cell size to control how big the cells are in the simulation:


  • Pigment cell: A cell is a small unit that all living things are made of. You and I are made of cells, and so is fish skin. Pigment cells are a special type of cell that contain pigment (color). Black and yellow pigment cells play a big role in creating patterns on zebrafish.
  • Mathematical model: A set of rules or equations that describes something in a mathematical way. On this website, the mathematical model is the rule that you pick that instructs black and yellow cells where to appear on the fish checkerboard.
  • Simulation: An imitation of a real-world system on a computer. You are simulating fish patterns on this website! Click here to see a simulation of a fish pattern that scientists created with computer coding and a mathematical model in current academic research at colleges.

Image Sources

Simulating Pattern Formation on Fish
Last updated August 3, 2020