Ed Yong in National Geographic:
The program running on Jennifer Hoyal Cuthill’s computer is deceptively simple. First, it creates a cylinder. As the cylinder grows, it sprouts branches, first to the left and then to the right, always at the same specified angle. Each of the branches then becomes a stem in its own right, producing its own branches according to the same rules. On they go, branches off branches off branches, four levels deep. The results look like the leaves of ferns, but they’re much more. They look a lot like an ancient group of creatures called rangeomorphs, which existed in a time before skeletons, shells, legs, mouths, guts, and nervous systems. They were just a few inches long, but in a planet dominated mostly by single-celled creatures, they represented one of the first experiments in building relatively large and complex bodies.
…The best-preserved of the rangeomorph fossils show beautiful patterns that seem to repeat at different scales, with smaller versions of the same shape branching off larger ones. In other words, they look like fractals. Palaeontologists have always described them as such, but more in a metaphorical way than a mathematical one. “It had been suggested that they look a bit fractal-like but that hadn’t been tested,” says Hoyal Cuthill. She used her skills in computer science to write a program that uses simple rules of branching and growing to churns out a wide variety of body shapes, which look remarkably like actual fossils. The program has just 28 parameters, including the angle of the branches, their curvature, and how quickly the stems grow. Tweak the parameters, and you get a wide rangeomorph zoo. “It’s a relatively simple program but it’s versatile enough to generate a good approximation of the things we observe in the fossil record,” says Hoyal Cuthill.