This is a process analogous to the repeated expression of a genetic code, which happens with each cell division. Organic forms such as the Mandelbrot set can be generated with this process. These forms are examples of fractals, and they are portraits of their own functions. Every individual fractal is one creature in a vast range of possible creatures. There are parts of their functions which can vary, and so they can be mutated and re-expressed to generate creatures with varying anatomies.
All fractals are members of a complex and infinite family tree.
A new taxonomy of related fractal families is being developed, led by geometers such as Clifford Pickover and Michael Barnsley. Richard Dawkins, in The Blind Watchmaker, describes the evolution of a species in terms of a range of possible genetic states. Necessity for that species to adapt to its environment limits the possibilities of its genetic states. If all the genes of that creature are considered as axes in a large multidimensional space, then its evolution can be seen as a trajectory in that space. The trajectory represents genetic mutations, and its general trend is towards better adaptability with its changing environment.