The natural world has always had a chaotic way about it. The mathematical
world has always been amazing complex. So why Chaos theory just evolved
as such a critical part of science, mathematics, art and computing world.
The calculations involved are repetitive, boring, and number in the millions.
To produce the Mandelbrot Set on a single screen takes an estimated
6,000,000 calculations. Nu human would be stupid enough to endure the
boredom. But a computer will. Computers are particularly good at mindless
repetition. The computer is our telescope, our microscope, and now, our art
gallery. We cannot really explore Chaos without it, and we certainly can't
produce fractals unaided.
However, it is necessary to use the computer as an investigative tool. Most
computer use is based on putting in data and instructing the computer on what
output is required. Chaos Theory arose as scientists and mathematicians
started to play. To put in numbers and watch as they careered around the
plane, mostly the complex plane, in detailed patterns. They watched as the
computer produced the numbers, and didn't just wait for the final result. And
they tried different ways of plotting and exploring equations- mostly for the fun
Playing with mathematicians, science and computer programming produced
images which looked like nature. Ferns and clouds and mountains and bacteria.
They indicated why we couldn't predict the weather. They seemed to match the
behavior of the stock exchange and populations and chemical reactions all at the
same time. Their investigations suggested answers to questions which had been
asked for centuries- about the flow of fluids as they moved from a smooth to
irregular flow, about the formation of snowflakes, about the swing of a pendulum,
about tides and heartbeats anc cauliflower and rock formations.
This new theory dealt with a vast range of intellectual domains. And they started
plotting the fractals. Some mimicked nature. Some were stunningly beautiful.
And some were just fascinating.
Chaotic Systems are not random. They may appear to be. They have some simple
1. Chaotic systems are deterministic. This means they have something determining their behavior.
2. Chaotic systems are very sensitive are very sensitive to the initial conditions. A very slight change in the starting point can lead to enormously different outcomes. This makes the system fairly unpredictable.
3. Chaotic systems appear to be disorderly, even random. But they are not. Beneath the random behavior is a sense of order and pattern. Truly random systems are not chaotic. The orderly systems predicted by classical physics are the exceptions. In this world of order, chaos rules!
There is a strong link between chaos and fractals. Fractal geometry is the geometry
which describes the chaotic systems we find in nature. Fractals are a language, a way
to describe geometry. Euclidean geometry is a description of lines, circles, triangles,
and so on. Fractal geometry is described in algorithms- a set of instructions on how
to create the fractal. Computers translate the instructions into the magnificent patterns
we see as fractal images.
If you would like to download some fractal images, please go to our download site.