This command-line application generates and visualizes the most popular fractals Mandelbrot set and the Julia set.

Mandelbrot set is defined as the set of complex numbers C such that: Z_n+1 = Z_n²+C, starting with Z₀ = 0 remains bounded when n reaches infinity. (When performing the caculation, instead of infinity the programme takes in an argument for the number of iterations which defaults to 1000) All Mandelbrot numbers are within a region of the complex plane; -1 < real part < 1 and -1 < complex part < 1. We call this the region of interest. These values can be passed to the programme (optional) separated with spaces in the above order. Last argument will be the number of interations.

A point on the display is first mapped onto a point within the region of interest. Once that is done that value is used as C and the above computation Z_n+1 = Z_n²+C is performed the specified number of iterations and then see if ABS(Zn) > 2 for any n < iterations. If so C is not a Mandelbrot number and therefor assign some colour to it based on value of n when ABS(Zn) > 2. Else assign black. This process is repeated for all points on the canvas.

The Julia set is similar to the Mandelbrot set in that it uses the same equation, but Z₀ is the point in the complex plane corresponding to the pixel and C is a constant. Real and imaginary parts of C can be passed (optional) as aguments to the programme separated with spaves, by default its value will be -0.4 + 0.6i.

To install llocally:

git clone https://github.com/KavinduJayas/fractals.git

cd fractals

javac Fractal.java

java Fractal [ Mandelbrot | Julia ] [args]

Class diagram of the Java implementation: