Mandelbrot Set in C/C++ Using Graphics

Fractals

A Fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Mathematically fractals can be explained as follows.

• The location of a point on a screen is fed into an equation as its initial solution and the equation is iterated a large number of times.
• If that equation tends to zero (i.e. the value at the end of the iterations is smaller than the initial value), the point is coloured black.
• If the equation tends to infinity (i.e. the final value is larger than the initial value) then depending on the rate of increase (i.e. the rate at which the value tends to infinity), the pixel is painted with an appropriate colour.

Defining Mandelbrot

The Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from z=0, i.e., for which the sequence , etc., remains bounded in absolute value. In simple words, Mandelbrot set is a particular set of complex numbers which has a highly convoluted fractal boundary when plotted. 👁 Image
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Implementation 

Output 👁 Image