equations, scientists modeled the Spot on computers and found that it was indeed a self-organizing system composed of chaotic atmospheric flow. If you look closely at movies constructed from successive photos taken by flyby missions past Jupiter, you will note its fractal nature. Eddies within eddies constantly break off and other eddies join it.

Watch this video

here:

Scientists model many other aspects of nature by testing simple equations on computers and plotting the results on Cartesian graphs. One of the most famous examples of this is the building of a fractal fern. The equations are loaded and the basic fern structure takes shape on the monitor. Leaves are added as the stem grows. Note the tinier leaves growing on tinier stems within the larger structures, and then yet even tinier structures filling in as fern leaves grow their own little leaves. The fern becomes astonishingly lifelike in form surprisingly quickly.

Watch a fractal fern grow here:

This reminds me of a poem that I though was written by Ogden Nash, but which was actually penned by Augustus De Morgan. It's a refinement of an even earlier poem by Jonathan Swift:

Great fleas have little fleas

Upon their backs to bite 'em

And little fleas have lesser fleas

And so ad infinitum

Scalar self-referential systems were familiar to scientists and intellectuals for centuries. But as computer graphics became ubiquitous in the Seventies and Eighties, scientists have had much more success modeling them.

Some fractals are built up over time on the computer's Cartesian graph program in an apparently haphazard way. As the computer runs the equation, solutions are posted on the graph in the form of dots. As the dots grow in number, a pattern emerges. The dots cluster around one, two, or more areas of the graph, areas mathematicians call Strange Attractors. Out of very simple equations, complexity grows.

Here are some startlingly beautiful examples of Strange Attractors:

Consider the most striking form of fractal: the Mandelbrot Set. Mandelbrot generated a collection of points on a graph by taking a series of complex numbers, squaring each of them, adding the original number to each, and squaring them again and again. If the number remains finite after many such iterations, it remains in the Set and is plotted on the graph.

The resulting shape is composed of successful solutions to what is truly an extraordinarily simple equation. Paradoxically or not, it's the most

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