Chaos is the science of detecting order in apparent randomness

Interdiciplinary in nature, it includes the fields of math, physics, biology, ecology, meteorology

Fundamental is the notion that nonlinear equations are sensitive to initial conditions

Defines new way to plot equations;
previous: to one value of x assign one value of y
new: iterate and feedbcack equation to determine how it behaves for a point in the xy plane

Ed Lorenz did early work by modeling weather by simple differential equations; resulted in the concept of the Butterfly Effect.

Mendelbrot is the giant of teh science of chaos; he invented notion of fractals and fractal dimension; wrote The Fractal Geometry of Nature; generated the "Mendelbrot Set"

Fractal shoreline: roughness the same regardless of the magnification; implies infinite length; implies length depends on amount of roughness

fractal: Pattern repeats on larger & smaller scale

Cantor Set: points infinite in number but infinitely sparse on a line

Julia Set

Kock Curve: infinite length in finite space

The Chaos Game
If you follow two rules randomly, the result is not random, but a pattern.

Great Red Spot of Jupiter is an example of order on chaos
Old Red Spot Theories: lava flow, new moon, egg floating in atmosphere; column of gas
in fact, the Red Spot drifts slightly against it's background, but does not drift far.
Voyager showed Red Spot to be a hurricane like swirl in the midst of a chaotic atmosphere
Questions: what keeps it going, what keeps it in place?
A new analog is the Gulf Stream
Marcus model: modeled Jovian weather by fluid dynamic equations;
This results in a Red Spot
planet spins fast, which causes a large Coriolus force
The Coriolus force drives the Red Spot