same complex assortment of bays and peninsulas. Which scale is best - miles, yards, feet, inches? A surveyor would be in a quandary. All measurements would be equally true, yet each would lead to a vastly different result.

Also, this scalar property of coastlines would make it particularly difficult to pinpoint the true nature of a specific portion of them without an outside reference. For instance, you can't tell if you're looking at a photo of the White Cliffs of Dover or an eroded outcropping of chalk a few feet high without, say, a human being standing next to it.

Mandelbrot's fractals consist of just these kinds of nested, repeating patterns. When you see a fractal built up from tinier and tinier triangles, its self-referential nature is quite unmistakable. The overall structure of triangles within triangles is repeated with some variations (or none at all) all the way to infinity.

We see fractal aspects of repetitive branchings and clumpings in a wide variety of natural objects and phenomena such as trees, lightning, and river watersheds. We see other aspects of fractal self-reference when water crystallizes in the winter sky, forming a growing tip, becoming unstable, and then sending branches out to form a snowflake.

Similar patterns can be seen in a clear glass of super-saturated sugar water. Add a string and watch sugar crystals grow. Window panes are painted with a forest of fractal frost on a cold winter's day. Create fractals on a stovetop. Boil water and vegetable oil in a saucepan. Let it cool. Note how oil puddles into fractal-like circles on the surface of the water. Sometimes they look like Julia sets as small archipelagoes of circles float next to larger circles.

When a chemist heats dyed viscous fluids that mix as poorly as oil and water, they begin to get wavy, tendrils form, which draw on themselves over and over again. Loops and marble-like whorls pinwheel, creating images of stunning beauty.

Jupiter's Great Red Spot is the most spectacular example of non-mixing fluids at work. This vast oval near the equator is actually a giant hurricane bigger than the Earth. It has lasted for centuries, never moves with respect to the other bands of dense hydrogen and helium of the planet, and despite the jostling, retains its overall characteristic shape.

The Spot was a mystery for years after it was first imaged. What could that apparently enormous structure be? Wouldn't such a thing collapse in on itself? Using fluid

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