Mitch Richling: Pickover Popcorn

Author:	Mitch Richling
Updated:	2022-12-10

1. Pickover Popcorn Fractals
2. Algorithms & Code
3. Gallery
4. References

1. Pickover Popcorn Fractals

Clifford Pickover's fractal popcorn is an an orbit-fractal traditionally using the following functions:

\[\begin{eqnarray} x & = & x - h \cdot \sin\left(y + \tan(a \cdot y)\right) \\ y & = & y - h \cdot \sin\left(x + \tan(b \cdot x)\right) \end{eqnarray}\]

Typical parameter choices are: \(a=0.3\), \(b=0.3\), and \(h=0.05\). The orbits tend to densely cover regions of the plane with swirling patterns.

Over time people have started calling any orbit fractal of similar form a Pickover Popcorn Fractal. Common modifications include replacing one or more of the trig functions with other trig functions.

2. Algorithms & Code

Note the code uses hstRamCanvas to count the number of times each pixel is hit – the counters are 16-bit unsigned integers. Then we use writeTIFFfile with a converter object to color the counts, and produce a nice image. Both the count and color image are saved – so you can load the counts image up in something like ImageJ and recolor it to your heart's content.

#include "ramCanvas.hpp"

// This is *identical* to what we did in sic.cpp -- just way shorter.
typedef mjr::ramCanvas1c16b::rcConverterColorScheme<mjr::ramCanvas1c16b, mjr::color3c8b, mjr::color3c8b::csCCfractal0RYBCW, true, 10, 0> g2rgb8;

int main(void) {
  std::chrono::time_point<std::chrono::system_clock> startTime = std::chrono::system_clock::now();
  const int    IMXSIZ = 7680/2;
  const int    IMYSIZ = 4320/2;
  const int    NUMITR = 100;
  const int    spanx  = 1;
  const int    spany  = 1;
  const double h      = 0.05;
  const double a      = 3.0;
  const double b      = 3.0;
  mjr::ramCanvas1c16b hstRamCanvas(IMXSIZ, IMYSIZ, -4.0, 4.0, -2.25, 2.25);

  for(int y=0;y<hstRamCanvas.getNumPixY();y+=spany) {
    if ((y%100)==0)
      std::cout << y << std::endl;
    for(int x=0;x<hstRamCanvas.getNumPixX();x+=spanx) {
      double zx = hstRamCanvas.int2realX(x);
      double zy = hstRamCanvas.int2realY(y);
      for(int i=0; i<NUMITR; i++) {
        double tmpx = zx - h * std::sin(zy + std::tan(a * zy));
        double tmpy = zy - h * std::sin(zx + std::tan(b * zx));
        zx = tmpx;
        zy = tmpy;
        int ix = hstRamCanvas.real2intX(zx);
        int iy = hstRamCanvas.real2intY(zy);
        if (hstRamCanvas.isOnCanvas(ix, iy))
          hstRamCanvas.getPxColorRefNC(ix, iy).tfrmAdd(1);
      }
    }
  }
  hstRamCanvas.writeTIFFfile("pickoverPopcornCNT.tiff");
  g2rgb8 rcFilt(hstRamCanvas);
  hstRamCanvas.writeTIFFfile("pickoverPopcornCOL.tiff", rcFilt, false);
  std::chrono::duration<double> runTime = std::chrono::system_clock::now() - startTime;
  std::cout << "Total Runtime " << runTime.count() << " sec" << std::endl;
  return 0;
}