Mitch Richling: Inverted Mandelbrot

Author:	Mitch Richling
Updated:	2022-09-13

1. Introduction
2. Algorithm & Code
3. References

1. Introduction

This is really just the Mandelbrot Set remapped to the complex plane via the reciprocal function. The \(\frac{1}{z}\) function turns the Mandelbrot Set inside out with the point \(0+0i\) mapping to \(\infty\) – so the Mandelbrot Set proper is the black space extending outside the teardrop and stretching out to infinity.

2. Algorithm & Code

#include "ramCanvas.hpp"

typedef mjr::ramCanvas3c8b::colorType ct;

int main(void) {
  std::chrono::time_point<std::chrono::system_clock> startTime = std::chrono::system_clock::now();
  const int NUMITR = 1024;
  const int IMXSIZ = 7680/2;
  const int IMYSIZ = 7680/2;

  mjr::ramCanvas3c8b theRamCanvas(IMXSIZ, IMYSIZ, -1.5, 4.25, -2.875, 2.875);

  for(int y=0;y<theRamCanvas.getNumPixY();y++) {
    for(int x=0;x<theRamCanvas.getNumPixX();x++) {
      std::complex<double> c(theRamCanvas.int2realX(x), theRamCanvas.int2realY(y));
      if (std::norm(c)>1e-5) {
        std::complex<double> z(0.0, 0.0);
        int count = 0; 
        c = 1.0 / c;
        while((std::norm(z)<50) && (count<=NUMITR)) {
          z=std::pow(z, 2) + c;
          count++;
        }
        if(count < NUMITR)          
          theRamCanvas.drawPoint(x, y, ct::csCColdeFireRamp::c(static_cast<ct::csIntType>(count*15)));
      }
    }
  }
  theRamCanvas.writeTIFFfile("invertedMandelbrot.tiff");
  std::chrono::duration<double> runTime = std::chrono::system_clock::now() - startTime;
  std::cout << "Total Runtime " << runTime.count() << " sec" << std::endl;
}

The above program will generate the following picture:

3. References

Check out the fractals section of my reading list.

All the code used to generate everything on this page may be found on github.

Mitch Richling: Inverted Mandelbrot

Table of Contents

1. Introduction

2. Algorithm & Code

3. References