🚀 go-pugleaf

In article 24563@sol.UVic.CA, aschoorl@engr.UVic.CA (Andre  Schoorl) writes:
> 
> Can anybody simply tell me what the equation of the Mandelbrot set is?
> Ever book I've ever seen expects you to know it before cracking the cover.
> 

I'm sure most readers will know this stuff in their sleep, but I remember
going through the same head-scratching just to get started, so I've included
mandel.c which contains the relevant info embedded in simple, working C code.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

			/* * * * * * * * * *\
			 * MANDEL.C        *
			 * by Daniel Green *
			\* * * * * * * * * */

#define BIG 100.0

#define NORMSQRD(zx,zy) (zx*zx+zy*zy)

/* complex addition */
#define PLUS(resultx,resulty, ax,ay, bx,by)  \
	(resultx = ax + bx, \
	 resulty = ay + by)

/* complex multiplication */
#define TIMES(resultx,resulty, ax,ay, bx,by)  \
	(resultx = ax*bx - ay*by, \
	 resulty = ay*bx + ax*by)

/* set to most natural floating point type */
typedef double Real;

/*
 * Iterates the Mandelbrot function Z = Z^2 + C where C is a point in
 * the complex plane, and Z is initially complex zero.  Iteration ends when
 * the magnitude of Z grows too large, or if the given maximum number
 * of iterations is reached (given point is then assumed to be in the set).
 *
 * Returns 0 if in the set, otherwise number of iterations to divergence.
 * Note: zx and zy are initialized to x and y, and the counter is initialized
 * to 1 because that is what they would always be after the first iteration
 * if they were all initialized to zero as they officially should be.
 */
int mandel(x, y, max_iterations)
Real x, y;
int max_iterations;
{
	register Real zx, zy, cx, cy, tempx, tempy;
	register int iterations;

	zx = cx = x;
	zy = cy = y;
	for (iterations = 1;
	     (NORMSQRD(zx,zy) < BIG) && (iterations < max_iterations);
	     iterations++) {
		TIMES(tempx,tempy, zx,zy, zx,zy);
		PLUS(zx,zy, tempx,tempy, cx,cy);
	}
	return iterations == max_iterations ? 0 : iterations;
}

---
Daniel Green
danielg@autodesk.com
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