README.md

About

Java multithreaded application, using MVC design pattern, which allows users to generate beautiful fractals. It lets users to conveniently zoom in/out and move center by mouse or keyboard, generate images and videos of mandelbrot set. Download

Theory

Mandelbrot set is a set of points in the complex plane for which the orbit of z_n doesn't tend to infinity. The iteration formula used in the Mandelbrot set is:

Z₀ = 0
Z_n+1 = Z_n² + C
Where C determines the location of the iteration series in the complex plane.

Calculating the Mandelbrot Set

• If the magnitude of Z ever becomes larger than declared threshold value, we will assume that it will diverge into infinity.
• If the number of iterations exceeds declared maximum iterations value, we will assume that Z doesn't tend to infinity.
• We will speed up calculations by using Divide and Conquer approach, calculating each part of set in different thread (Can be easily implemented with Fork/Join in java)

Coloring the plot

In order to colorize the plot we take number of iterations performed and map that against a color spectrum.
Color smoothing equation can be found here: http://linas.org/art-gallery/escape/smooth.html

Zooming

Zooming is achieved by decreasing/increasing mandelbrot set range

Examples

Click here for more examples