Here are some fish. Each can be made from the others by applying anisotropic and/or inhomogenous growth rules:

The sandpit program below begins with a basic fish, and allows you to apply distortions of growth in the y direction, according to position on the x axis (in this example, there is no way to alter growth in the x axis). Growth in the y direction can be constant, or a linear function of x position, or an exponential function of x position, or a harmonic function of x position, or a function of y position. These can be applied in any combination: you can do this by altering terms in the governing equation in the sandpit. In the starting condition, most variables are set to zero so that most available distortions are not applied. They begin to be applied when you alter a value from zero.

Play with the parameters and try to make the fish above.

**Please note**: the above simulation runs requires a browser that can launch
java applications. You may find that this application is blocked by a security
setting - this is not because the application is sinister, but because it is
'unsigned'. Reduce your java security to 'medium' (for at least this one
application). If you are completely stuck, you can down-load this
software in stand-alone form by clicking here.

When you are ready to finish, click here.