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In the pub on Friday I was reminded of the little ray tracer I hacked up while at University, and I couldn't resist tinkering with it a bit the next day. Unfortunately the code has gone moldy over the past few years, but while I was looking at it I found another little hack I did a while ago.

This isn't something I discovered. I found the formula on the Grotesque Geometry website (under ‘grotesque geometry I’), which credits it to Gary Tupper of Pedagoguery Software. Anyway, here's what it looks like:

full size: 1280×1024, 418Kb

What's surprising is how interesting and wibbly this picture is, given that it's just a plot of some simple trigonometry. Here's the expression which is used to calculate the intensity at each point:

sin(x * (cos(y) - cos(x))) + sin(x) - sin(y)

My little program (in C) to generate it is below. It uses the image plotting and output code from my ray tracer, which is why I found it among the wreckage of that project, but it should be obvious how to change it to use any other image library.

#include "image.h"
#include <string.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>

/* Spidery wibbly picture generator.
 * Geoff Richards, 2002-2003.
 * Do what you want with this code.  There's no warranty.
 *
 * Good example: ./spider 1280 1024 30
 *
 * Based on a forumla found here: http://www.cromp.com/tess/
 */

int
main (int argc, char **argv)
{
    SilsnaImage *img;
    int width, height;
    double zoom;
    int x, y;
    double xf, yf;
    double v;
    int mono;
    SilsnaFColor c;
    int scale;
    int i;

    if (argc != 4 && (argc != 5 || strcmp(argv[1], "--mono"))) {
        fprintf(stderr, "Usage: %s [--mono] WIDTH HEIGHT ZOOM\n", argv[0]);
        return 1;
    }
    i = 1;
    if (argc == 5)
        mono = 1, ++i;
    else
        mono = 0;
    width = atoi(argv[i++]);
    height = atoi(argv[i++]);
    zoom = atof(argv[i++]);
    scale = width > height ? width : height;

    img = silsna_img_new(width, height, 1, mono ? 1 : 8);

    for (y = 0; y < height; ++y) {
        for (x = 0; x < width; ++x) {
            xf = ((double) x / scale - 0.5) * zoom;
            yf = ((double) y / scale - 0.5) * zoom;

            v = sin(xf * (cos(yf) - cos(xf))) + sin(xf) - sin(yf);

            if (mono)
                silsna_img_set_pixel_mono(img, x, y, v < 0);
            else {
                c.r = c.g = c.b = (v + 1) / 2;
                c.a = 1;
                silsna_img_set_pixel_f(img, x, y, &c);
            }
        }
    }

    if (mono)
        silsna_img_write(img, "spider.pbm", SILSNA_FILETYPE_PBM, 0);
    else
        silsna_img_write(img, "spider.pgm", SILSNA_FILETYPE_PGM, 0);

    return 0;
}

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