You might think that the more random something is, the more complex it is. But computer scientists measure complexity by how hard it is to model something. Completely ordered things like crystals have low complexity, but so do completely disordered things, because you can easily model them with randomness. Fractals however are half-way between completely ordered and completely disordered. Self-organizing systems like living things and turbulence give rise to the most complex patterns and behaviors. Fractals are a "signature" of self-organization.