lifef/fractals

Fracrals

Introduction:

You are required to design and implement a software that would plot two of the most popular fractals: Mandelbrot set and Julia set. Fractals are infinity many, self-similar shapes formed by some simple mathematical computations. The computation varies from fractal set to set but are generally based on complex numbers.

The Mandelbrot set:

In mathematics Mandelbrot set is defined as the set of complex numbers C such that: Z n+1 = (Zn)^2 + C , starting with Z0 = 0 remains bounded when n reach infinity. In other words if for some C the above equation remains bounded for after many iterations then that C is in the Mandelbrot set. There is a mathematical proof which shows that if ABS(Zn) > 2 the above equation will diverge hence C is not in the Mandelbrot set. Some complex numbers will be in the Mandelbrot set and some are not.

• To genatare Mandelbrot set image Mandelbrot -Rx1 Rx2 -Iy1 Iy2 NumberOfIteration

Rx1 Lower Boundary of x range

Rx2 Upper Boundary of x range

Iy1 Lower Boundary of y range

Iy2 Upper Boundary of y range Of Canvas

The Julia set:

The Julia set is similar to the Mandelbrot set in that it uses the same equation Zn+1 =(Zn)^2 + C but Z0 is the point in the complex plane corresponding to the pixel and C is a constant. The rest of the computation is the same; including the way you map a point in the canvas to that in the complex plane.

• To geanrate the Julia Set image Julia -RealPartOfZ ImaginaryPartOfZ NumberofIteration

-1 < Real(Z) < 1

-1 < Img(Z) < 1

Output