Barricelli's Evolutionary Universe Simulator
This simulation system was originally run by the mathematician Nils Barricelli on the computer at the Institute for Advanced Study in the 1950s during free cycles overnight. He intended it to be a synthetic demonstration of a number of concepts he was thinking about in evolutionary biology, described in detail in this paper:
Barricelli, Nils Aall. Numerical testing of evolution theories. Part I. Theoretical Introduction & Basic Tests. Acta Biotheoretica, vol. 16, nos 1-2, 69–98.
Aside from this, it's also an interesting demonstration of simple cellular automata from which an awe-inspiringly complex ecosystem of interactions freely emerges. With the addition of a color scheme it has the potential to create some strikingly beautiful images.
Written in Python with NumPy and matplotlib.