Fractals--a PBS production
What do movie special effects, the stock market, and heart attacks have in common? All three are connected by a revolutionary new branch of mathematics called fractals, which changed the way we see the world and opened up a vast new territory to scientific analysis and understanding. Meet the mathematicians who developed fractals from a mere curiosity to an approach that touches nearly every branch of understanding, including the fate of our universe. Check out the new DVD that PBS has released about fractals to get a better understanding of this branch of mathematics.
A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced sized copy of the whole--a property known as self-similarity. A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
Because they appear similar on all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountains, lightning bolts, coastlines and snowflakes.
Fractals are prevalent in art as well as in nature. Fractal patterns have been found in the paintings of Jackson Pollack--the patterns in his paintings appear to be random dripping or splattering, but computer analysis has found fractal patterns. Decalcomania, a technique used by artists like Max Ernst also produce fractal like patterns. Decolcomania involves a process of pressing paint between two surfaces and pulling them apart. Fractals are also very common in African art.
For more information on fractals visit this Yale University site.
An example of a naturally occuring fractal: