Mitch Richling: Mandelbrot Biomorph
| Author: | Mitch Richling |
| Updated: | 2022-10-11 |
Table of Contents
1. Introduction
I'm calling this the Mandelbrot Biomorph Fractal, but I made that name up! It's really just the Mandelbrot Set with color schemes and iteration stop conditions inspired by biomorph fractals.
In the traditional Mandelbrot set, iteration stops when \(\vert z\vert > 2\). In the code, iteration stops when \(\vert\Re(z)\vert \ge 10\) and \(\vert\Im(z)\vert \ge 10\). As for the color schemes, we have six of them. Only the first one uses just the iteration count. The rest use \(z\) or the next to last \(z\) value.
2. Algorithm & Code
#include "ramCanvas.hpp" typedef mjr::ramCanvas3c8b::colorType ct; typedef ct::csIntType cit; 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; const int LIM = 10; mjr::ramCanvas3c8b theRamCanvasA(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); mjr::ramCanvas3c8b theRamCanvasE(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); mjr::ramCanvas3c8b theRamCanvasK(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); mjr::ramCanvas3c8b theRamCanvasL(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); mjr::ramCanvas3c8b theRamCanvasM(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); mjr::ramCanvas3c8b theRamCanvasN(IMXSIZ, IMYSIZ, -2.75, 2.75, -2.75, 2.75); for(int y=0;y<theRamCanvasA.getNumPixY();y++) { for(int x=0;x<theRamCanvasA.getNumPixX();x++) { std::complex<double> c = theRamCanvasA.int2real(x, y); std::complex<double> z(0.0, 0.0); std::complex<double> zL(0.0, 0.0); int count = 0; while( ((std::abs(std::real(z))<LIM) || (std::abs(std::imag(z))<LIM)) && (count<NUMITR) ) { zL = z; z=std::pow(z, 2) + c; count++; } if(count < NUMITR) { // A theRamCanvasA.drawPoint(x, y, ct::csCColdeRainbow::c(static_cast<cit>(count*500))); // E if(std::abs(std::real(z))<std::abs(std::imag(z))) theRamCanvasE.drawPoint(x, y, ct("red")); else theRamCanvasE.drawPoint(x, y, ct("blue")); // K theRamCanvasK.drawPoint(x, y, ct::csCColdeRainbow::c(static_cast<cit>((std::arg(z)+3.14)*255))); // L if(std::abs(std::real(z))<std::abs(std::imag(z))) theRamCanvasL.drawPoint(x, y, ct::csCCu0R::c(mjr::intClamp(static_cast<cit>(std::abs(std::real(z))*15), ct::csCCu0R::numC-1))); else theRamCanvasL.drawPoint(x, y, ct::csCCu0B::c(mjr::intClamp(static_cast<cit>(std::abs(std::imag(z))*15), ct::csCCu0B::numC-1))); // M if(std::abs(std::real(zL)) < LIM) theRamCanvasM.drawPoint(x, y, ct::csCCfractalYB::c(std::abs(std::real(zL))/LIM)); else if(std::abs(std::imag(zL)) < LIM) theRamCanvasM.drawPoint(x, y, ct::csCCfractalYR::c(std::abs(std::imag(zL))/LIM)); else theRamCanvasM.drawPoint(x, y, "white"); // N if(std::abs(std::real(zL)) < LIM) theRamCanvasN.drawPoint(x, y, ct::csCCdiag01::c(std::abs(std::real(zL))/LIM)); else if(std::abs(std::imag(zL)) < LIM) theRamCanvasN.drawPoint(x, y, ct::csCCdiag10::c(std::abs(std::imag(zL))/LIM)); else theRamCanvasN.drawPoint(x, y, "white"); } } } theRamCanvasA.writeTIFFfile("mandelbrot_biomorphA.tiff"); theRamCanvasE.writeTIFFfile("mandelbrot_biomorphE.tiff"); theRamCanvasK.writeTIFFfile("mandelbrot_biomorphK.tiff"); theRamCanvasL.writeTIFFfile("mandelbrot_biomorphL.tiff"); theRamCanvasM.writeTIFFfile("mandelbrot_biomorphM.tiff"); theRamCanvasN.writeTIFFfile("mandelbrot_biomorphN.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 all of the images in the gallery below.
3. Gallery