fractals

Fractals are endlessly complex patterns that are self-similar across different scales.

The Mandelbrot set is a kind of map of how multiplication and addition interact with each other in the complex numbers. It is one of the first iterative math functions calculated and displayed by computers by Benoit Mandelbrot in the 1970s.

mandelbrot.c

void
mandel(Uint32 *dst)
{
	int width = 640, height = 480, max = 254;
	int row, col;
	for(row = 0; row < height; row++) {
		for(col = 0; col < width; col++) {
			double c_re = (col - width / 1.5) * 4.0 / width;
			double c_im = (row - height / 2.0) * 4.0 / width;
			double x = 0, y = 0;
			Uint32 iteration = 0;
			while(x * x + y * y <= 4 && iteration < max) {
				double x_new = x * x - y * y + c_re;
				y = 2 * x * y + c_im;
				x = x_new;
				iteration++;
			}
			putpixel(dst, col, row, (iteration % 2) * 0xFFFFFF);
		}
	}
}

Mandelbrot without fixed point

See the complete SDL2 source.

mandel(-2.0 * NORM_FACT, -1.2 * NORM_FACT, 0.7 * NORM_FACT, 1.2 * NORM_FACT);

typedef unsigned char Uint8;
typedef signed char Sint8;
typedef unsigned short Uint16;
typedef signed short Sint16;

#define NORM_BITS 8
#define NORM_FACT ((Sint16)1 << NORM_BITS)

Uint16 WIDTH = 600;
Uint16 HEIGHT = 400;

int
iterate(Uint16 real0, Uint16 imag0)
{
	Uint8 i;
	Sint16 realq, imagq, real = real0, imag = imag0;
	for(i = 0; i < 255; i++) {
		realq = (real * real) >> NORM_BITS;
		imagq = (imag * imag) >> NORM_BITS;
		if((realq + imagq) > (Sint16)4 * NORM_FACT)
			break;
		imag = ((real * imag) >> (NORM_BITS - 1)) + imag0;
		real = realq - imagq + real0;
	}
	return i;
}

void
mandel(Sint16 realmin, Sint16 imagmin, Sint16 realmax, Sint16 imagmax)
{
	Uint16 x, y,
		deltareal = (realmax - realmin) / WIDTH,
		deltaimag = (imagmax - imagmin) / HEIGHT,
		real0 = realmin,
		imag0;
	for(x = 0; x < WIDTH; x++) {
		imag0 = imagmax;
		for(y = 0; y < HEIGHT; y++) {
			putpixel(pixels, x, y, iterate(real0, imag0));
			imag0 -= deltaimag;
		}
		real0 += deltareal;
	}
}