Nature looks chaotic at first glance, but close observation reveals repeating geometric algorithms at work. The branching of a river delta mirrors the branching of a tree, which mirrors the branching of your circulatory system — because they all solve the same geometric problem: distributing resources with maximum efficiency.
A fractal exhibits self-similarity at every scale. Each part contains a miniature version of the whole. A natural coastline has a fractal dimension around 1.25, meaning it is more complex than a line but not quite a surface.
Natural selection favors structures that maximize functional surface area within a constrained volume. Your lungs pack the surface area of a tennis court through 23 generations of fractal branching. Fractals are solutions to resource distribution problems.
Fractals reveal that nature's apparent complexity often emerges from simple rules applied repeatedly at different scales. The universe builds complexity from simplicity through iteration.