 Fractals are self-similar objects that, sometimes, are all around us.
A simple example could be the branches in a tree. They are self-similar in many ways. A big branch looks similar to a small branch and vice versa.
Fractals became "famous" around 1985 when the first picture in a magazine was published in the cover of Scientific American. Fractal theory is a branch of Pure Mathematics and now a days, the theory behind these amazing pictures, is becoming useful in other fields such as Computer Science and Physics. The most famous fractal picture is the Mandelbrot set, named after Benoit Mandelbrot, an IBM scientist who studied the phenomena and began using computer graphics to represent the very simple formulas that generate these pictures. The Mandelbrot set is actually a representation of real and imaginary parts of an equation of complex numbers. Complex numbers were invented by Mathematicians because they couldn't compute  ,
like they could  . So they invented the solution for the root of -1 to be i (imaginary numbers).
A complex number is represented like z = a + bi, where a and b are Real numbers. A complex number z, has two parts: a real element and an imaginary element. This becomes interesting, since we can now view a complex number as a vector with 2 elements, hence, we can represent them graphically like a vector in 2D. For example, if wanted to plot z = 2 + 2i, we can do so as follows:  Why is this vector representation important for fractals? Follow the next page ». |
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