Benoit B. Mandelbrot (born November 20, 1924, Warsaw, Poland—died October 14, 2010, Cambridge, Massachusetts, U.S.) was a Polish-born French American mathematician universally known as the father of fractals.
The software was developed to generate specific parts of the famous Mandelbrot set.
The output files of the program are 800x600 binary .ppm images. The RGB value of each pixel is determined by the amount of iterated value divergence, which is calculated using the following formula and starting parameters:
$$c.Re = x_{pixel}; c.Im = y_{pixel}$$ $$z_{0}.Re = 0; z_{0}.Im = 0$$
$$\sum_{i=0}^{n} z_{i+1} = z_{i}^2 + c$$
$$\text{where } n = \text{number of iterations}$$
Below are the images and the command with its parameters used to create them:
./fractal.out <img>.ppm <x_min> <y_min> <x_max> <y_max> <num_of_iter>
./fractal.out fractal001.ppm -2.0 1.0 3.0 2.0 30
./fractal.out fractal002.ppm -0.75 0.12 0.01 0.01 100
./fractal.out fractal003.ppm -0.925 0.266 0.01 0.01 100
./fractal.out fractal004.ppm -1.25066 0.02012 0.0001 0.0001 400
./fractal.out fractal005.ppm -1.25 0.02 0.001 0.001 400
./fractal.out fractal006.ppm 0.2671 -0.003 0.002 0.002 100
./fractal.out fractal007.ppm 0.2817 0.5770 0.0002 0.0002 125
./fractal.out fractal008.ppm -0.8407 0.2244 0.0002 0.0002 100
./fractal.out fractal010.ppm 0.25 0.05 0.1 0.1 100
./fractal.out fractal011.ppm -0.805 0.18 0.01 0.01 100
./fractal.out fractal012.ppm -0.815 0.1809 0.05 0.05 100
./fractal.out fractal013.ppm 0.317 0.042 0.01 0.01 100
Of course, there were some development attempts that didn’t quite make the cut, showcasing the trial and error of fractal creation journey. But their presence was crucial as they indicated progress toward success:
