Do you need to be told about chaos, or is your bedroom a permanent example? As everyone knows, beneath what those intolerably neat and tidy people consider to be chaos, there is a form of order. The chaotic housekeeper can always find the item of their desire - as long as no-one tidies up! Many systems which scientists have considered totally random, unpredictable and without form have now been found to be otherwise. There is form and pattern hidden within the CHAOS. It is a part of the natural form - a definitive ingredient of Nature itself.   The Oxford Concise Dictionary defines chaos as "Formless primordial matter; utter confusion."

The day has come when there is a need for an update - Chaos Theory is changing the way scientists look at the weather, the way mathematicians plot equations and the way artists define Art. Population dynamics is one area which can be very sensitive to small changes in initial conditions. So can the weather. A butterfly flapping its wings in a South American jungle, it is said, can lead to a hurricane in China. This is the signature of Chaos Theory! Think about the "new" disease, AIDS. Somewhere, sometime, maybe, a cell mutated. Think about the number of cells there are in the world. This was a pretty tiny event. BUT it happened to be a crucial mutation. Somewhere, somehow, the cell multiplied and spread. Or, maybe, the disease first moved into the human race - one infection. In terms of the population of the earth, a very small event.

Something determined the spread of this disease. From a tiny change in initial conditions a disease took a huge toll. There was a mechanism, a necessary set of conditions so the spread was not completely random. But it was unpredictable. Many other such mutations or infections must have occurred but had little or no effect. That tiny event somewhere led to large percentages of some populations to be struck down. It changed the nature of the whole human population. The butterfly of AIDS flapped its wings somewhere in Africa and cause a hurricane across the world.

As scientists studied these systems, a mathematics evolved which had already drawn interest from pure mathematicians. This mathematics involved ITERATION - taking the answer to the equation and feeding it back into the equation, over and over again. In watching the result of this process, some fascinating behaviours were observed. When the mathematicians and scientists got together, with the benefit of machines which could do their calculations within minutes, a new science was born.

In playing with these ideas, a new way of doing science grew. These computers could not only calculate they could communicate too. Information flew around the globe. You no longer had to be in the right place or talk to the right people. The equipment and information was available to masses of people all over the world. And their mathematics produced images which were stunningly beautiful, and, at times, awesomely like nature. A new art form was born and a whole new set of questions arose about the nature of nature itself. These images, called FRACTALS, were fun. They had an ever growing fan club who became obsessed with their generation.

Science, maths, computing, philosophy, art - where will Chaos end? Nowhere and never, we hope!

The Nature of Chaos

The natural world has always had a chaotic way about it. The mathematical world has always had amazing complexity resulting from simple equations. So why has Chaos theory just evolved as such a critical part of science, mathematics, art and the computing world?

A simple answer: computers.

The calculations involved are repetitive, boring and number in the millions. To produce the Mandelbrot Set on a single screen takes, it is estimated, about 6,000,000 calculations. No 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 our art gallery. We cannot really explore Chaos without it, and we certainly can't produce fractals unaided.

But 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 of it.   A fractal forgery of a landscape - mathematically generated on a  computer.

Playing with mathematics, 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 behaviour 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 move from a smooth to a turbulent flow, about the formation of snowflakes, about the swing of a pendulum under the influence of magnets, about tides and heartbeats and cauliflower and rock formations and the behaviour of Hyperion.
 
This new theory was infiltrating a vast range of intellectual domains. And then they started plotting the fractals. Some mimicked nature. These caused a stir. Some were stunningly beautiful. These created a debate: Was this Art? And some were just fascinating. Mandelbrot and Julia became the jargon of a new group of enthusiasts. 

Chaotic systems are not random. They may appear to be. They have some simple defining features:

1. Chaotic systems are deterministic. This means they have some determining equation ruling their behaviour. 2. Chaotic systems 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 seemingly random behaviour is a sense of order and pattern. Truly random systems are not chaotic.