Amazing Fractals: Hunting the Hidden Dimension. Here's an entire PBS Nova episode
If you don't understand what fractals are or how they are created, you ain't 21st century! Mendlebrot will surely win a Nobel Prize for discovering them and defining them mathematically.
Hunting the Hidden Dimension. You may be familiar with fractals, but in this PBS Nova episode, divided online into 5 parts, fractals go beyond the impossible zoom of the Mandelbrot set. Scientists are using fractals to describe complex natural occurrences, like lava, capillaries, and rain forests. In part 5, scientists measure one tree in the rain forests, and the distribution of small and large branches mirror the distribution of small and large trees. Fractals, it seems, are nature.