Question

Abstract: Can you propose a mathematical-ish algorithm over a plane of pixels that will generate a moderately interesting image, preferably one that on the whole resembles something?

The story thus far:

Once upon a time I decided in an effort to reduce cycle waste on my (admittedly too) numerous computers, and set out to generate images in a moderately interesting fashion; using a PRNG and some clever math to create images that would, on the whole, resemble something.

Or at least, that was the plan. As it turns out, clever math requires being a clever mathematician; this I am not.

At some length I arrived at a method that preferred straight lines (as these are generally the components of which our world is made), perhaps too strongly. The result is mildly interesting; resembling, perhaps, city grids as such:

City grids, maybe? http://totlandweb.info/imggen.out.png

Now for the question proper: Given the source code of this little program; can you improve upon it and propose a method that gives somewhat more interesting results? (e.g. not city grids, but perhaps faces, animals, geography, what have you)

This is also meant as a sort of challenge; I suppose and as such I’ve set down some completely arbitrary and equally optional rules:

1. The comments in the code says it all really. Suggestions and “solutions” should
   edit the algorithm itself, not the surrounding framework, except as for to fix
   errors that prevents the sample from compiling.

2. The code should compile cleanly with a standard issue C compiler. (If the
   example provided doesn’t, oops! Tell me, and I’ll fix. 🙂

3. The method should, though again, this is optional, not need to elicit help from
   your friendly neighborhood math library, and on the whole employ a (P)RNG as its
   primary data input channel.

4. Solutions should probably be deliverable by simply yanking out whatever is between
   the snip lines (the ones that say you should not edit above and below, respectively),
   with a statement to the effect of what you need to add to the preamble in particular.

5. Edit: It is sometimes easy to forget that people on the internet cannot read my
   mind; but there you go. The program should require a minimum of human intervention in
   the generation of the images, except for to evaluate the results and chose the best
   ones.

The code requires a C compiler and libpng to build; I’m not entirely confident that the MinGW compiler provides the necessities, but I would be surprised if it didn’t. For Debian you’ll want the libpng-dev package, and for Mac OS X you’ll want the XCode tools..

The source code can be downloaded here.

Warning: Massive code splurge incoming!

// compile with gcc -o imggen -lpng imggen.c
// optionally with -DITERATIONS=x, where x is an appropriate integer
// If you're on a Mac or using MinGW, you may have to fiddle with the linker flags to find the library and includes.

#include <stdio.h>
#include <stdlib.h>
#include <png.h>

#ifdef ITERATIONS
#define REPEAT
#endif // ITERATIONS

// YOU MAY CHANGE THE FOLLOWING DEFINES
#define WIDTH 320
#define HEIGHT 240

// YOU MAY REPLACE THE FOLLOWING DEFINES AS APPROPRIATE
#define INK 16384

void writePNG (png_bytepp imageBuffer, png_uint_32 width, png_uint_32 height, int iteration) {
  char *fname;
  asprintf(&fname, "out.%d.png", iteration);

  FILE *fp = fopen(fname, "wb");
  if (!fp) return;
  png_structp png_ptr = png_create_write_struct(PNG_LIBPNG_VER_STRING, NULL, NULL, NULL);
  png_infop  info_ptr = png_create_info_struct(png_ptr);
  png_init_io(png_ptr, fp);
  png_set_filter(png_ptr, PNG_FILTER_TYPE_DEFAULT, PNG_FILTER_NONE);
  png_set_compression_level(png_ptr, Z_BEST_COMPRESSION);
  png_set_IHDR(png_ptr, info_ptr, width, height, 8,
               PNG_COLOR_TYPE_GRAY, PNG_INTERLACE_NONE, PNG_COMPRESSION_TYPE_DEFAULT, PNG_FILTER_TYPE_DEFAULT);
  png_set_rows(png_ptr, info_ptr, imageBuffer);
  png_set_invert_mono(png_ptr); /// YOU MAY COMMENT OUT THIS LINE
  png_write_png(png_ptr, info_ptr, PNG_TRANSFORM_IDENTITY, NULL);
  png_destroy_write_struct(&png_ptr, &info_ptr);
  fclose(fp);
  free(fname);
}

int main (int argc, const char * argv[]) {
  png_uint_32 height = HEIGHT, width = WIDTH;


  int iteration = 1;
#ifdef REPEAT
  for (iteration = 1; iteration <= ITERATIONS; iteration++) {
#endif // REPEAT  

    png_bytepp imageBuffer = malloc(sizeof(png_bytep) * height);
    for (png_uint_32 i = 0; i < height; i++) {
      imageBuffer[i] = malloc(sizeof(png_byte) * width);
      for (png_uint_32 j = 0; j < width; j++) {
        imageBuffer[i][j] = 0;
      }
    }    

    /// CUT ACROSS THE DASHED LINES
    /// -------------------------------------------
    /// NO EDITING ABOVE THIS LINE; EXCEPT AS NOTED

    int ink = INK;
    int x = rand() % width, y = rand() % height;

    int xdir = (rand() % 2)?1:-1;
    int ydir = (rand() % 2)?1:-1;

    while (ink) {
      imageBuffer[y][x] = 255;
      --ink;
      xdir += (rand() % 2)?(1):(-1);
      ydir += (rand() % 2)?(1):(-1);
      if (ydir > 0) {
        ++y;
      } else if (ydir < 0) {
        --y;
      }
      if (xdir > 0) {
        ++x;
      } else if (xdir < 0) {
        --x;
      }
      if (x == -1 || y == -1 || x == width || y == height || x == y && x == 0) {
        x = rand() % width; y = rand() % height;
        xdir = (rand() % 2)?1:-1;
        ydir = (rand() % 2)?1:-1;
      }
    }

    /// NO EDITING BELOW THIS LINE
    /// -------------------------------------------

    writePNG(imageBuffer, width, height, iteration);

    for (png_uint_32 i = 0; i < height; i++) {
      free(imageBuffer[i]);
    }    
    free(imageBuffer);
#ifdef REPEAT
  }
#endif // REPEAT
  return 0;
}

Note: While this question doesn’t strictly speaking seem “answerable” as such; I still believe that it can give rise to some manner of “right” answer. Maybe.

Happy hunting.

Edit (again): The source code for the simplistic bezier paths used in my answer (read down) can be found here and here.

Answer 1

Fractals? They’re not just for stock markets analysis anymore (Mandelbrot joke, sorry).

Some Fractal images tend to be reminiscent of real-world geographies. In particular IFS fractals can be used for fairly realistic plants and trees, and terrain.

fractal.c is a simple monochromatic Mandelbrot set, at its default zoom.

---

Added:

Context-free grammars can be used to express equations that can draw images that are aesthetically pleasing to humans. Jared Tarbell has a related gallery of some wonderful images generated by programs. Aza‘s Algorithm Ink

2nd addition:

The other major form of algebraic or computation art is from Cellular automaton (CA), such as (John) Conway’s Game of Life, made famous by the 1970 Scientific American article written by Martin Gardner. CA was re-introduced to the public with Stephen Wolfram’s self-publication of A New Kind of Science (NKS) in 2002. These tend to be closed dynamic systems, that “live” or “die” based on a simple set of rules.

Related to fractals are chaotic systems, or non-linear dynamic systems if you want to sound smart. They can be modelled on physical systems, like weather forecasting, and can provide not-really-random but hard-to-predict numeric output that can be visualized as a strange attractor (and SA).