Image:Tricorn.png

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Full resolution‎ (1,024 × 1,024 pixels, file size: 43 KB, MIME type: image/png)

[edit] Summary

The tricorn (a fractal similar to the Mandelbrot set), plotted in the area [−2, 2) × [−2, 2). The value of each pixel equals 255 minus the number of iterations needed before the absolute value of z becomes larger than 2, calculated at the upper left corner of the pixel.

The following C code was used to create a negative PGM image:

#include <stdio.h>
#include <limits.h>
main() {
unsigned int resx = 4096, resy = 4096;  //Resolution;
unsigned char i = 0;                    //Iteration counter;
float xmin = -2, xmax = +2;             //Borders of the area
float ymin = -2, ymax = +2;             //to be plotted;
unsigned int xpix = 0, ypix = 0;        //Column and row counters;
float x, y;                             //Coordinates;
long double Rez, Imz, Rez_new, Imz_new; //Real and imaginary parts.
FILE *f;

f = fopen("tricorn.pgm", "w");
fprintf(f, "P2\n%d %d\n%d\n", resx, resy, UCHAR_MAX); //Portable Greymap file header
for (ypix = 0; ypix < resy; ypix++) {
        for (xpix = 0; xpix < resx; xpix++) {
                x = xmin + xpix * (xmax - xmin)/resx;
                y = ymin + ypix * (ymax - ymin)/resy;
                Rez = x; Imz = y;
                for (i = 0; Rez*Rez + Imz*Imz <= 4; i++) { //z = conj(z^2) + c
                        Rez_new = Rez*Rez - Imz*Imz + x;       //(It'd be z = z^2 +c for Mandelbrot)
                        Imz_new = -2*Rez*Imz + y; //remove minus sign here to obtain the Mandelbrot set
                        Rez = Rez_new;
                        Imz = Imz_new;
                        if (i == UCHAR_MAX) break; }
                fprintf(f, "%d ", i); }
        fprintf(f, "\n"); }
}

Then I used the GIMP to invert colors, reduce to 25% and save it as PNG.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. Subject to disclaimers. This file is licensed under the Creative Commons Attribution-ShareAlike license versions 2.5, 2.0, and 1.0. You may select the license of your choice.

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