Mandelbrot set ASCII art

mandelbrot.c

/*
 * Mandelbrot set ascii art
 */

#include <stdio.h>
#include <string.h>

/* Params */
//TODO: these should be command line arguments

const int COLUMNS = 151, LINES = 53;
const float CENTRE_X = -0.6, CENTRE_Y = 0;
const float STEP = 0.045; // in y direction

// threshold to accept a point as in the set
// increase this when the step is small (high zoom)
const int MAX_ITERS = 200;

// points not in the set are shaded by how fast they diverge
// cyclic list of chars to use for different divergence speeds
const char palette[] = "Patrick!<3";


/*
 * Determines whether a point is in the Mandelbrot set
 * params: float ptX, float ptY: x and y coords of the point
 * returns: int number of iterations to reject the point (MAX_ITERS if accepted)
 */
int getRejectionIters(const float ptX, const float ptY)
{
	float re = 0, im = 0, reSq = 0, imSq = 0;
	int nbIters = 0;
	
	// iterate z <- z^2 + pt
	// until |z|>2 (diverging) or the point is accepted
	while (imSq + reSq <= 4 && nbIters < MAX_ITERS)
	{
		im = 2*re*im + ptY;
		re = reSq - imSq + ptX;
	
		imSq = im*im;
		reSq = re*re;
	
		nbIters++;
	}

	return nbIters;
}

/*
 * Writes a single character representing a point
 * params: float ptX, float ptY: x and y coords of the point
 */
void drawPoint(const float ptX, const float ptY)
{
	int rejectionIters;
	
	rejectionIters = getRejectionIters(ptX, ptY);
	
	if (rejectionIters >= MAX_ITERS) // point in set
	{
		printf(" ");
	}
	else // point not in set; shade by divergence speed
	{
		printf("%c", palette[(rejectionIters - 1) % strlen(palette)]);
	}
}

int main()
{
	// character aspect ratio is 2:1 on my terminal
	const float STEP_X = STEP / 2, STEP_Y = STEP;
	
	int curCol, curLine;
	float ptX, ptY;
	
	// iterating over point coords directly risks rounding errors
	for (curLine = 0 ; curLine < LINES ; curLine++) // y-coord, decreasing
	{
		ptY = CENTRE_Y + (0.5 * LINES - curLine - 0.5) * STEP_Y;
		
		for (curCol = 0 ; curCol < COLUMNS ; curCol++) // x-coord, increasing
		{
			ptX = CENTRE_X - (0.5 * COLUMNS - curCol - 0.5) * STEP_X;
			
			drawPoint(ptX, ptY);
		}
		printf("\n");
	}
	
	return 0;
}