Fractals are an important part of chaos theory, which is crucial to understanding physics at many, perhaps all, levels. Chaos theory is often one of the more misunderstood portions of modern physics. A chaotic function or system is not the same as a random one-thus, chaos theory does not explain the randomness in quantum physics. Rather, a chaotic system is one in which the resulting action of the system is widely divergent from a very small divergence in initial conditions. That is, displacement by a tiny fraction of a percent of the measurement used will cause results that diverge by orders of magnitude.

Chaotic behavior can occur in both classical and quantum mechanical systems. The physical world has many examples of chaotic behavior, from magnetic pendula to planets orbiting double star systems. Each system follows known equations of motion, but each system is heavily reliant on the position...