XXIIVV — fractals

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

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;
	}
}