Fractals can be used to describe the spreading of substances, such as gases diffusing or oil spilling in water. One of the ways this can be modeled is using what are called diffusion fractals. In order to make a diffusion fractal, you need to start from the center and spread the points outwards. The way this is done is by randomly moving points around the screen, similarly to real-life molecules’ Brownian motion. When a point hits the center point, you make it stay there permanently. When some other point hits either the center point, or the new point, you make it stay as well. What you see when the shape is being formed is something like this:

Similarly, this can be used to model not only diffusion, but the spilling of oil in water as well. Benoit Mandelbrot also found a similarity between the spilling of water and the formation of a Quadric Koch Island: