Mandelbrot Set! (GitHub link included!)

GitHub – Mandelbrot Set

UPDATE: I have now written a Zoom Sequence Generator driver program. With that, you can create videos like https://www.youtube.com/watch?v=YfE8wf7N0qg and https://www.youtube.com/watch?v=3pCIyW4cQNA. Visit the GitHub repository to know more!

The MandelBrot Set is “a particular set of complex numbers which has a highly convoluted fractal boundary when plotted.” Mathematically speaking, define a sequence z such that:  and Then the Mandelbrot set is the set of all numbers c such that 

I have written a program in C++ that generates a .bmp image of the required coordinates of the Mandelbrot Set! It is fully customizable in terms of:

• Region of the set you want (real coordinates, imaginary coordinates)
• Number of iterations
• Colour of the image

You can enter commands for many images at once. It is up for download and/or testing on GitHub here. Right now, I am working on the shading algorithm for the colors. (Currently, I am using a quartic polynomial shading, which tends to make images purple-ish) Here are some cool images from the program:

The entire Mandelbrot Set.

(RealAxis -2 to 1, ImaginaryAxis -1 to 1, 50 iterations per pixel)

 

A part of the fractal that resembles lightning bolts.

(RealAxis -0.04 to -0.03, ImaginaryAxis 0.98 to 0.99, 50 iterations per pixel)

 

Many smaller copies of the entire structure exists inside the main structure. This is one of them.

(RealAxis -1.420 to -1.415, Imaginary Axis -0.0025 to 0.0025, 200 iterations per pixel)

 

The entire Mandelbrot Set rendered in pink.

(RealAxis -2 to 1, ImaginaryAxis -1 to 1, 50 iterations per pixel)

An “elephant trunk” from the “elephant valley”

(RealAxis 0.27707 to 0.28165, ImaginaryAxis 0.00627 to 0.01085, 200 iterations per pixel)

 

 

Some other images-

You will find the input commands for all these images over at github.

I have also made an animated GIF of the 3rd image above, as the iteration count goes from 50 to 200. Please be patient while it loads, as it is a rather large image (around 50MB). View it here. (Bluish bands around the boundaries are compression artifacts)