Search NOVA Teachers

Back to Teachers Home

Hunting the Hidden Dimension

Program Overview

NOVA explores the fascinating world of fractals and looks at how they can be used to better understand everything from coastlines and rainforests to weather systems and human physiology.

The program:

  • reports on one of the first applications of fractal geometry—when a Boeing computer scientist in 1978 applied principles of fractal geometry to create a mountain background for a plane for publicity photos.

  • introduces Benoît Mandelbrot's realization that many forms in nature can be described mathematically as "fractals," a word he invented to describe shapes that look jagged, or broken, or that do not conform to traditional geometry.

  • explains that fractals are produced by taking a smooth-looking shape and dividing it repeatedly in a process known as iteration.

  • describes one of the defining characteristics of a fractal—self-similarity—a state in which an object looks the same regardless of the distance from which it is viewed, or in which an object's parts look similar to the whole object.

  • notes that prior to Mandelbrot's discovery of fractal geometry in the 1970s, mathematicians relied on classical mathematics to describe geometric shapes but had no mechanism for characterizing the erratic patterns that existed in nature.

  • recounts that while he was working at IBM, Mandelbrot noticed patterns in phone-line transmissions that reminded him of a hundred-year-old mystery known as mathematical "monsters."

  • illustrates some of the monsters, including the Cantor set, Koch's snowflake, and the Julia set.

  • shows how Mandelbrot used the Julia set to create his own equation, which, when iterated and graphed on a computer, generated the well-known Mandelbrot set.

  • notes that many pure mathematicians turned against Mandelbrot when his work first appeared, and that even today some mathematicians maintain that his work has done little to advance math theory.

  • presents some of the many ways fractals are used and applied to everyday life, including measuring coastlines, creating special effects in film, downsizing wire antennas, better understanding human physiology, and investigating why large animals use energy more efficiently than small ones.

  • follows researchers to a Costa Rican rainforest, where they try to determine whether applying fractal geometry to data from a single tree can reveal information about how much carbon dioxide the entire rainforest can absorb.

Taping Rights: Can be used up to one year after program is recorded off the air.

Teacher's Guide
Hunting the Hidden Dimension