tile.jpg FRACTAL FIND
Explore Fractal and Quantum Variations

Lynn Wienck

APPENDIX D
Tile Variations

Tile Variations use modified Mandelbrot configurations with pixels plotted at count increment.
Example Tile with Pseudocode
Example Tile ft.jpg
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
Tile #1 ft.jpg
Tile #2 ft.jpg
Tile #3 ft.jpg
Tile #4 ft.jpg
Tile #5 ft.jpg
Tile #6 ft.jpg
Tile #7 ft.jpg
Tile #8 ft.jpg
Tile #9 ft.jpg
Tile #10 ft.jpg
Tile #11 ft.jpg
Tile #12 ft.jpg
Tile #13 ft.jpg
Tile #14 ft.jpg
Tile #15 ft.jpg
Tile #16 ft.jpg
Tile #17 ft.jpg
Tile #18 ft.jpg
Tile #19 ft.jpg
Tile #20 ft.jpg
Tile #21 ft.jpg
Tile #22 ft.jpg
Tile #23 ft.jpg
Tile #24 ft.jpg