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Ok. Fractals are related to chaos because they are complex systems that have definite properties. Fractals depict chaotic behaviour because they are are non-linear and irregular. They are beyond simple geomtry such as circle or a straight line. The shape/length of a fractal is infinite. You can zoom in on a section of a fractal and it will have just as much detail as the whole fractal. The behaviour is infinite.
Take a tree, for example. Pick a particular branch and look at it closely. Choose a bundle of leaves on that branch. To chaologists, all three of the objects described - the tree, the branch, and the leaves - are identical. To many, the word chaos suggests randomness, unpredictability and perhaps even messiness. Chaos is actually very organized and follows certain patterns. The problem arises in finding these patterns.
By looking at a fractals we can predict patterns in dynamical systems that on the surface seem unpredictable. A system is a set of things,- an area of study -A set of equations is a system, such as weather systems, the movement of water currents, or animal migration patterns.
Weather is a good example. Ok so forecasts are never totally accurate, and long-term forecasts, even for one week, can be totally wrong. This is because of minor disturbances in airflow, solar heating, etc. Each disturbance may be minor, but the change it create will increase geometrically with time. Soon, the weather will be far different than what was expected.
"The summit is just a halfway point"
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