Fractal Find : Explore Fractal and Quantum Variations

APPENDIX D
Tile Variations

Tile Variations use modified Mandelbrot configurations with pixels plotted at count increment.

xnew = f(x,y) + cos(xs) - sin(ys)
ynew = g(x,y) - cos(xs) - sin(ys)

Example Tile with Pseudocode

for (int i = 0; i ≤ 800; i++)
{
	oldk = 0;
	for (int j = 0; j ≤ 800; j++)
	{
		x = 0.0;
		y = 0.0;
		xs = -4.0 + i / 100.0;
		ys = -4.0 + j / 100.0;
		k = 0;
		do
		{
			k++;
			xnew =  x*y*y+cos(xs)-sin(ys);
			ynew = -y*x*x-cos(xs)-sin(ys);
			x = xnew;
			y = ynew;
		} while (x*x+y*y ≤ 16.0 && k ≤ kmax);
		if (oldk != k) PlotPixel(i, j, color);
		oldk = k;
	}
}
for (int j = 0; j ≤ 800; j++)
{
	oldk = 0;
	for (int i = 0; i ≤ 800; i++)
	{
		x = 0.0;
		y = 0.0;
		xs = -4.0 + i / 100.0;
		ys = -4.0 + j / 100.0;
		k = 0;
		do
		{
			k++;
			xnew =  x*y*y+cos(xs)-sin(ys);
			ynew = -y*x*x-cos(xs)-sin(ys);
			x = xnew;
			y = ynew;
		} while (x*x+y*y ≤ 16.0 && k ≤ kmax);
	if (oldk != k) PlotPixel(i, j, color);
	oldk = k;
	}
}

Tile	Build: (f(x, y), g(x, y))	Escape: h(x, y) > value
Example	(x * y * y - cos(xs) + sin(ys), -x * x * y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #1	(x * x - y * y - cos(xs) + sin(ys), x * x * y - cos(xs) - sin(ys))	x + y > 8.0
Tile #2	(x * y - cos(xs) - sin(ys) * 2 * x, x * y - cos(xs) - sin(ys) * 2 * y * x)	x + y > 8.0
Tile #3	(y - x * x - cos(xs) + sin(ys), -x * x * y * y - y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #4	(y - x * x - cos(xs) + sin(ys), -x * x * y * y - y - cos(xs) - sin(ys))	x + y > 8.0
Tile #5	(-x * y * k / 8 + cos(xs) - sin(ys), -y * x * k / 8 - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #6	(x * y - y - cos(xs) + sin(ys), x * y - x - cos(xs) - sin(ys))	x + y > 8.0
Tile #7	(x * y - cos(xs) + sin(ys) * y, x * y - cos(xs) - sin(ys) * x)	x + y > 8.0
Tile #8	(x * x - y * y - cos(xs) + sin(ys), -x + y - cos(xs) - sin(ys))	x + y > 8.0
Tile #9	(-x * x * y * k / 8 + cos(xs) - sin(ys), -y * x * k / 8 - cos(xs) - sin(ys))	x² + y² > 16.0/k
Tile #10	(x * y * y + x - cos(xs) + sin(ys), -x * y * y + y + x - cos(xs) - sin(ys))	x + y > 8.0
Tile #11	(x * y * y - x + y + cos(xs) - sin(ys), -y * x * x - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #12	(-x * y * y - 0.5 * x - cos(xs) + sin(ys), -y * x * x - y - cos(xs) - sin+(ys))	x² + y² > 16.0
Tile #13	(x * x + y * y - cos(xs) + sin(ys), -x - y - cos(xs) - sin(ys))	x + y > 8.0
Tile #14	(x * y * y + y * x + cos(xs) - sin(ys), -y * y * x + x * y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #15	(x * y * y - x - cos(xs) + sin(ys), -y * x * x - y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #16	(x * y * y + y * x + cos(xs) - sin(ys), -y * y * x + x - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #17	(x * y * y + y + cos(xs) - sin(ys), -y * y * x + x - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #18	(x * y * y + cos(xs) - sin(ys), -y * y * x + x - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #19	(x * y * y + cos(xs) - sin(ys), -y * y * x + x + y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #20	(x * x * y * y - x - cos(xs) + sin(ys), -y * x * x - y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #21	(x * y * y - x + cos(xs) - sin(ys), ynew = -y * y * x + x + y - cos(xs) - sin(ys))	x² + y² > 16.0
Tile #22	(x * y * y - y + cos(xs) - sin(ys), -y * y * x + x + y - cos(xs) - sin(ys))	x*² + y² > 16.0
Tile #23	(y * x * x - x * y * y - cos(xs) + sin(ys), -8.0 * x * y - cos(xs) - sin(ys))	x + y > 8.0
Tile #24	(x * y * y + x + y + cos(xs) - sin(ys), -y * y * x - x - cos(xs) - sin(ys))	x²*y² > 16.0