Peter de Jong Everywhere All At Once

Author:	Mitch Richling
Updated:	2025-02-19

1. Introduction
2. Code
3. References

1. Introduction

Normally when working with the Peter de Jong map we pick a set of parameters (a-h), pick a seed point, and iterate the map. As we iterate a few million times recording all the points the map visits in the plane. Usually we just count the number of times the map hits each pixel, or region, and use that count to colorize the result. Not much thought is normally given to the choice of the initial seed point, and many people always use zero. This approach is used in the example peterdejong.cpp. A write up of this example may be found here:

https://www.mitchr.me/SS/swirl/index.html

I called this example "Peter de Jong Everywhere All At Once" because we are using a grid of seed points and simultaneously doing the above process for each pixel in an image. We don't iterate millions of times – just 8 in this case. Then we colorize the result not by hit count, but by the value of the map at each pixel.

2. Code

#include "ramCanvas.hpp"
#include "MRMathSTR.hpp"
#include "MRMathIVL.hpp"

int main(void) {
  std::chrono::time_point<std::chrono::system_clock> startTime = std::chrono::system_clock::now();
  const int    IMXSIZ = 7680/1;
  const int    IMYSIZ = 7680/1;

  const int    n =  8;
  const double a =  1.4;
  const double b =  2.3;
  const double c =  2.2;
  const double d =  1.9;
  const double e =  1.1;
  const double f =  2.1;
  const double g =  1.1;
  const double h = -2.3;

  mjr::ramCanvas1c64F xcanvas(IMXSIZ, IMYSIZ, -2, 2, -2, 2);
  mjr::ramCanvas1c64F ycanvas(IMXSIZ, IMYSIZ, -2, 2, -2, 2);
  for(int itr=0; itr<n; itr++) {
#   pragma omp parallel for schedule(static,1)
    for(int yi=0;yi<xcanvas.getNumPixY();yi++) {
      for(int xi=0;xi<xcanvas.getNumPixX();xi++) {
        double x, y;
        if (itr == 0) {
          x = xcanvas.int2realX(xi);
          y = xcanvas.int2realY(yi);
        } else {
          x = xcanvas.getPxColorRefNC(xi, yi).getC0();
          y = ycanvas.getPxColorRefNC(xi, yi).getC0();
          double xNew = std::sin(a*y + e) - std::cos(b*x + f);
          double yNew = std::sin(c*x + g) - std::cos(d*y + h);
          x = xNew;
          y = yNew;
        }
        xcanvas.drawPoint(xi, yi, x);
        ycanvas.drawPoint(xi, yi, y);
      }
    }
    std::cout << "ITR(" << itr <<  "): " << "DONE" << std::endl;
  }

  mjr::ramCanvas3c8b p1canvas(IMXSIZ, IMYSIZ);
  mjr::ramCanvas3c8b p2canvas(IMXSIZ, IMYSIZ);
  mjr::ramCanvas3c8b p3canvas(IMXSIZ, IMYSIZ);
  mjr::ramCanvas3c8b p4canvas(IMXSIZ, IMYSIZ);
# pragma omp parallel for schedule(static,1)
  for(int yi=0;yi<p1canvas.getNumPixY();yi++) {
    for(int xi=0;xi<p1canvas.getNumPixX();xi++) {
      double x = xcanvas.getPxColorRefNC(xi, yi).getC0();
      double y = ycanvas.getPxColorRefNC(xi, yi).getC0();

      double r = mjr::math::ivl::wrapCO((x+2)/4, 1.0);
      double g = 0.0;
      double b = mjr::math::ivl::wrapCO((y+2)/4, 1.0);
      p1canvas.getPxColorRefNC(xi, yi).setChansRGB_dbl(r, g, b);

      g = mjr::math::ivl::wrapCO((x+y+4)/8, 1.0);
      p2canvas.getPxColorRefNC(xi, yi).setChansRGB_dbl(r, g, b);

      p3canvas.drawPoint(xi, yi, decltype(p1canvas)::colorType::csPLYgrey::c(g));

      p4canvas.drawPoint(xi, yi, decltype(p1canvas)::colorType::csCColdeFireRamp::c(r*r));
    }
  }
  p1canvas.scaleDownMean(4);
  p2canvas.scaleDownMean(4);
  p3canvas.scaleDownMean(4);
  p4canvas.scaleDownMean(4);
  p1canvas.writeTIFFfile("peterdejongEAAO_00_c1.tiff");
  p2canvas.writeTIFFfile("peterdejongEAAO_00_c2.tiff");
  p3canvas.writeTIFFfile("peterdejongEAAO_00_c3.tiff");
  p4canvas.writeTIFFfile("peterdejongEAAO_00_c4.tiff");

  std::chrono::duration<double> runTime = std::chrono::system_clock::now() - startTime;
  std::cout << "Total Runtime " << runTime.count() << " sec" << std::endl;
  return 0;
}

Source Link: peterdejongEAAO.cpp

The above program will generate the following images:

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.

Peter de Jong Everywhere All At Once

Table of Contents

1. Introduction

2. Code

3. References