In the 1960's a biologist invented the Lindenmayer
system, which involves an initial axiom that is
successively modified according to given rules. Quite by
accident, it turns out that this system can be used to generate certain fractals,
which
I call Lindenmayer fractals. (A fractal is a pattern that is infinitely
complex; that is, upon enlarging a portion of the fractal image, more complexity
is
revealed, and the same is true for a portion of *that* image, and
so on ad infinitum.)

This project explains the Lindenmayer system, and demonstrates its usage in producing fractals. It also explains how computer software can be written to automate this production process.

In addition, the dimension of a fractal is explored. We find a definition of the dimension of an object that, for any Lindenmayer fractal, produces a single value for its dimension; however, this value is not necessarily an integral. In fact, we will see that the dimension of almost all fractals is irrational.