A chaotic washing machine? This is just what Goldstar Co. created back in 1993. It was the world's first consumer product to exploit "chaos theory", which holds that there are identifiable and predictable movements in nonlinear systems. This washing machine is supposed to produce cleaner and less tangled clothes. The key to the chaotic motion is a small pulsator (which stirs the water) that rises and falls randomly as the main pulsator rotates. When released to the world market, it was expected to push Goldstar's share of the annual 1.5-million-unit washing machine market to 40% in 1993, compared to 39% for Samsung and 21% for Daewoo (Goldstar's major competitors). However, marketing is fierce in South Korea and Daewoo argues that Goldstar "was not the first" to commercialize chaos theory. Daewoo also built a "bubble machine" in 1990 which also used chaos theory that was the result of "fuzzy logic circuits." Fuzzy circuits make choices between zero and one, and between true and false. These factors control the amount of bubbles, the turbulence of the machine, and even the wobble of the machine. It is clear that chaos theory has not gone unnoticed in today's consumer world market.

According to respected authorities, stock markets are non-linear, dynamic systems. Chaos theory is the mathematics of studying such non-linear, dynamic systems. Chaos analysis has determined that market prices are highly random, but with a trend. The amount of the trend varies from market to market and from time frame to time frame. A concept involved in chaotic systems is fractals. Fractals are objects which are "self-similar" in the sense that the individual parts are related to the whole. A popular example of this is a tree. While the branches get smaller and smaller, each is similar in structure to the larger branches and the tree as a whole. Similarly, in market price action, as you look at monthly, weekly, daily, and intra day bar charts, the structure has a similar appearance. Just as with natural objects, as you move in closer and closer, you see more and more detail. Another characteristic of chaotic markets is called "sensitive dependence on initial conditions." This is what makes dynamic market systems so difficult to predict. Because we cannot accurately describe the current situation band because errors in the description are hard to find due to the system's overall complexity, accurate predictions become impossible. Even if we could predict tomorrow's stock market change exactly (which we can't), we would still have zero accuracy trying to predict only twenty days ahead.
A number of thoughtful traders and experts have suggested that those trading with intra day data such as five-minute bar charts are trading random noise and thus wasting their time. Over time, they are doomed to failure by the costs of trading. At the same time these experts say that longer-term price action is not random. Traders can succeed trading from daily or weekly charts if they follow trends. The question naturally arises how can short-term data be random and longer-term data not be in the same market? If short-term (random) data accumulates to form long-term data, wouldn't that also have to be random? As it turns out, such a paradox can exist. A system can be random in the short-term and deterministic in the long term.

A long, long time ago, fractal god Benoit Mandelbrot posed a simple question: How long is the coastline of Britain? His mathematical colleagues were miffed, to say the least, at such an annoying waste of their time on such insignifigant problems. They told him to look it up.
Of course, Madelbrot had a reason for his peculiar question. Quite an interesting reason. Look up the coastline of Britain yourself, in some encyclopedia. Whatever figure you get, it is wrong. Quite simply, the coastline of Briutain is infinite.
You protest that this is impossible. Well, consider this. Consider looking at Britain on a very large-scale map. Draw the simplest two-dimensional shape possible, a triangle, which circumscribes Britain as closely as possible. The perimeter of this shape approximates the perimeter of Britain.
However, this area is of course highly inaccurate. Increasing the amount of vertices of the shape going around the coastline, and the area will become closer. The more vertices there are, the closer the circumscribing line will be able to conform to the dips and the protrusions of Britain's rugged coast.
There is one problem, however. Each time the number of vertices increases, the perimeter increases. It must increase, because of the triangle inequality. Moreover, the number of vertices never reaches a maximum. There is no point at which one can say that a shape defines the coastline of Britain. After all, exactly circumscribing the coast of Britain would entail encircling every rock, every tide pool, every pebble which happens to lie on the edge of Britain. Thus, the coastline of Britian is infinite.

Weather prediction is part of every new service. Three, maybe four days ahead. And sometimes they're right. But what about a week ahead, or a month? Naturally, Chaos scientists had a go at this problem. Their conclusions are not going to be much more use if you want to choose a fine day for your birthday party in three months!
There are many variables associated with the weather: temperature, air pressure, wind speed, wind direction, humidity and many more. The equations which control the weather involve all of these variables.
You can accurately put all these variables in an equation and calculate, with some degree of certainty the value of all the variables one second hence. These answers can be fed back in, and the values for the next second can be calculated one second hence. These answers can be fed back in, and the values for the next second can be calculated. Leave the poor computer go for long enough to do the iterations and you will know the weather one month later. Or will you?
Edward Lorenz tried this. Lorenz decided to run the program for longer. To do so he entered the values for halfway through the run and set the machine off again. But, the results soon deviated from the previous run. Lorenz found the reason was that he had put the values in accurate to three decimal places. The computer had calculated to six places. So a difference of one in a thousand was enough to change the output significantly. We can't measure the variables accurately enough to avoid the effects of chaos.
For ten years, Lorenz's paper on this result was ignored, despite Lorenz being aware that this was a crucial discovery. When he plotted the three key variables in three dimensional space, he gained a plot that came to be known as the Lorenz Attractor.

Construct a simple system: take a box, a simple solid rectangular solid. Within this box, place a gaseous substance. Heat the box, sit back, and watch. What happens to the gas? Everyone knows that warm gases rise while cooler gases sink; and initially, the portions of the gas closest to the walls of the box will become heated and rise. At certain temperatures, the gas will begin to form cylindrical rolls spaced like jelly rolls lying lengthwise in the box. On one side of the box, the gas rises, and on the other, it sinks; the rising gases move to one side and carry warmer gases up with them; as the gas cools, it falls on the other side of the box. With a regularly applied temperature, a smooth box interior, and a system completely closed with regards to the gas itself, it might be expected that the circular motion of the moving gas should be regular and predictable. Nature, however, is neither regular nor predictable. It turns out that the motion of the gas is chaotic. The rolls do not simply roll around and around in one direction like a steam-roller; they roll for a while in one direction, and then stop and reverse directions. Then, seemingly at random, the gas reverses direction again; these changes continue at unpredictable times, at unpredictable speeds.

Chaos theory isn't new to astronomers. Most have long known that the solar system does not "run with the precision of a Swiss watch." Astronomers have uncovered certain kinds of instabilities that occur throughout the solar system -- in the motions of Saturn's moon Hyperion, in gaps in the asteroid belt between Mars and Jupiter, and in the orbits of the system's planets themselves. As used by astronomers, the word chaos denotes an abrupt change in some property of an object's orbit. An object behaving in a chaotic manner may, for example, have an orbital eccentricity that varies cyclically within certain limits for thousands or even millions of years, and then abruptly its pattern of variation changes. The result is a sharp break in the object's history -- its past behavior no longer says anything about its long-term future behavior. For centuries astronomers tried to compare the solar system to a gigantic clock around the sun. But they found that their equations never actually predicted the real planets' movement. This problem arises from two points, one theoretical, and the other, practical. The theoretical difficulty was summed up by the work of French mathematician Henri Poincare around the turn of this century. He demonstrated that while astronomers can easily predict how any two bodies -- Earth and the Moon, for example -- will travel around their common center of gravity, introducing a third gravitating body (such as another planet or the Sun) prevents a definitive analytical solution to the equations of motion. This makes the long-term evolution of the system impossible, in principle, to predict. The practical difficulty are the limits of computer power. Even with the help of calculators and desktop computers, the long-term calculations were too lengthy. The conclusion from all this is that while new real-life chaos discoveries are being made, current computing technology can not keep up with the pace.