what is the chaos theory?

Answer 1

Chaos theory is a branch of mathematics dealing with equations whose solutions are highly sensitive to initial conditions. It has application for many physical problems with these characteristics such as weather patterns and celestial mechanics. Typically, any small change in initial conditions results in a solution which diverges from the original solution exponentially with time. This renders the future state virtually unpredictable in detail beyond a certain time. Often though, general trends *are* predictable (like seasons).

Answer 2

'Chaos' and 'Theory' are two words that when used together is an oxymoron. They mean exactly the opposite of each other. Mathematicians use the phrase because it sounds more exciting than "Advanced Modeling".
There are two basics regions of the study: one presumes that among the apparent randomness, some patterns may be found. The other presumes a system so random that it must stand outside of patterns. The first is simply an agglomeration of algorithms that form an ever-increasing loop around the events, trying to extract patterns. The second takes advantage of the fact that no patterns are present, and creates probable future behavior from the little which can be grasped.
For example, if the tossing of a coin were truly random for 'heads or tails', then it would first come up heads, then tails, then repeat this function forever. But, tossing it from the top of a tall building still has a field of environmental factors which provide patterns: the coin may only travel so fast through the air, has a maximum times it can spin before it lands, has aerodynamics surfaces which can be modeled... since it is finite, it can be modeled.
To a fool, a scientist's ability to pick the results of a hundred coin tosses off a tall building would be chaos theory. As computers get larger and the field of randomness gets smaller, chaos theory is moving toward the second, random study.

Answer 3

Chaos theory is basically a mathematical theory which states that things which appear chaotic (in the normal English sense rather than the mathematical one) often have a very simple underlying basis. A good example is the Mandelbrot set which is based on a simple equation (z*=z²+c). Recalculating this repeatedly, substituting z* for z at each iteration, then plotting the result produces the famous Mandelbrot image, as seen almost everywhere since it was first discovered in 1985. Zoom in to this image and the basic shape is repeated again and again, in theory for ever. In practice the theory can be shown to be the basis of many natural processes including the growth of trees and our planet's weather systems.

Answer 4

The chaos theory states that everything that happens has a result and an effect on the next thing to happen etc I.e a
kaleidescope or a cascasde or a waterfall.
IOt means that the world is always changing and we cannot change that. WEven out in outer space some people (including me) believe that the chaos theory has an effect.

Answer 5

An example may help. If you swing a common pendulum you can predict the (back and forth) motion. However if you swing a pendulum that is free to move in all directions, has a steel bob and is located over a triangular set of magnets the motion of the pendulum will describe a chaotic path. The path will depend greatly upon the initial condition (height and location of bob release relative to magnets) and then upon the influence of the magnets. Although the path may seem arbitrary parts of the path are nearly repeatable. Chaotic math attempts to describe the likely path(s). Click on the applet.

Answer 6

I think of it this way.

Imagine dropping a tennis ball off the roof. Each time you do it, it would bounce up to about the same height. If you increased the height, or threw it harder, you would get around the same bounce and you should be able to roughly predict the outcome with slight changes.

Chaos theory is like a game roulette. If you spin the ball, it may end up in 17. If you very slightly changed how hard you span it, it wouldn't go to 16 or 18, but to 5 or 27. The very slightest change gives a completely different outcome, unrelated to the slight change.

This gives the famous scenario that the smallest change of a butterfly flapping its wings could cause millions of other changes, resulting in the hurricane across the globe.

Answer 7

Chaos theory is based on "Entropy" - the notion that things can only get worse.

For example, you can drop a cup and the molecules will split very easily - but there's no process by which a broken cup can be fixed by the addition of energy alone. So the system (the structure of the cup) can get worse easily (by dropping it), but can't be easily fixed...

Answer 8

chaos theory: It has been said that something as small as the flutter of a butterfly's wing can ultimately cause a typhoon halfway around the world...

Answer 9

Out of chaos comes order.

Answer 10

just to sum up it says that very complex systems are not predictable.....

the best known example is the butterfly effect on the atmosphere, that says that a butterfly wing flip in china can lead to a hurricane months later in florida for instance....