tile.jpg FRACTAL FIND
Explore Fractal and Quantum Variations

Lynn Wienck

APPENDIX K
Wallpaper Variations

Wallpaper Variations use modified Mandelbrot configurations with pixels plotted at count increment.
Example Wallpaper with Pseudocode
The example shown here is the same as the Appendix D example.
Example Wallpaper wall.jpg
for (int i = 0; i ≤ 800; i++)
{
	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);
		PlotPixel(i, j, color);
	}
}
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
Wallpaper #1 (-x * x * y + cos(xs) - sin(ys), y * x * x - cos(xs) - sin(ys)) x*x + |y| > 16.0 / k
Wallpaper #2 (x * y + cos(xs) - sin(ys), x * y - cos(xs) - sin(ys)) x² + y² > 16.0/k
Wallpaper #3 (x + cos(x * x * y - x) + cos(xs) - sin(ys), y + sin(x * y) - cos(xs) - sin(ys)) x² + y² > 16.0
Wallpaper #4 (-x * y * y + cos(xs) - sin(ys), -y * x * x - cos(xs) - sin(ys)} |x| + |y| > 16.0 / k
Wallpaper #5 (x * y * y -x + cos(xs) - sin(ys), y * x * x - cos(xs) - sin(ys)) |x| + |y| > 16.0 / k
Wallpaper #6 (-x * x * y + cos(xs) - sin(ys), ynew = y * x - cos(xs) - sin(ys)) |x| + |y| > 16.0 / k
Wallpaper #7 (x * x * x * x - x * y * y * y + cos(xs) - sin(ys), -y * y * y * y - x * x * x * y - cos(xs) - sin(ys)) x² + y² > 16.0
Wallpaper #8 (y * x * x - x * y * y + cos(xs) - sin(ys), -y * y * y - x * x * x * y - cos(xs) - sin(ys)) x² + y² > 16.0
Wallpaper #9 (x * y * y + cos(xs) - sin(ys), y * x * x - cos(xs) - sin(ys)) x*x*y + y > 16.0
Wallpaper #10 (x * y * y + cos(xs) - sin(ys), y * x * x - cos(xs) - sin(ys)) |x| > 16.0 / k
Wallpaper #11 (-x * y * y + cos(xs) - sin(ys), y * x - cos(xs) - sin(ys)) |x| > 4.0 / k
Wallpaper #12 (-x * x * y +x + cos(xs) - sin(ys), y * x - cos(xs) - sin(ys)) |x| > 4.0 / k
Wallpaper #1 wall.jpg
Wallpaper #2 wall.jpg
Wallpaper #3 wall.jpg
Wallpaper #4 wall.jpg
Wallpaper #5 wall.jpg
Wallpaper #6 wall.jpg
Wallpaper #7 wall.jpg
Wallpaper #8 wall.jpg
Wallpaper #9 wall.jpg
Wallpaper #10 wall.jpg
Wallpaper #11 wall.jpg
Wallpaper #12 wall.jpg