Newton-fractal-generator

Given a complex polynomial, generate an image using Newton's method.

x^3 - 1 in the range [-1,1]X[-1,1]

To generate this, run ./newtonfractal

This project allowed me to learn

• C++ object oriented programming
• How to generate ppm images in C++
• regex
• Interpreting command line arguments

To build, just run make.

To run, ./newtonfractal [polynomial coefficients].

Images are generated as .ppm files

Command line arguments

By default, the program generates the above image:

• 512x512 pixel resolution

• Draws a 2.0x2.0 rectangle in the complex plane

• The top left of this rectangle is at -1+1i

• Pixels are coloured according to the default palette

• Pixels are shaded according to iteration depth

• Max iteration depth of 4000

• -v: verbose output

• -c [coefficients]: control what polynomial is generated, coefficients should go in ascending order of powers of x, separated by spaces, and each coefficient should be of the form x+yi or x-yi. The regex for a valid coefficient is "(.*)([+-].*)i".

• -pw [integer]: pixel width of output image

• -ph [integer]: pixel height of output image

• -o [complex number]: complex coordinates of the top left corner of the image, given in the same format as in -c

• -cw [double]: width of rectangle in complex plane

• -ch [double]: height of rectangle in complex plane

• --noshading: basins of attraction now one solid colour, not shaded according to iteration depth

• --maxdepth: maximum iteration depth before returning error - raising will reduce runtime, while increasing will reduce number of white artifacts in image

Future features

• Exponential smoothing of the image to blend different shades of the same regions together
• Multiprocessing support to divide the image into sections to generate concurrently