tile.jpg FRACTAL FIND
Explore Fractal and Quantum Variations

Lynn Wienck

CHAPTER 2
Tile Variations

c01.jpg c02.jpg
Mandelbrot Set with Pseudocode
for (int i = 0; i ≤ 500; i++)
{
	for (int j = 0; j ≤ 500; j++)
	{
		x = 0.0;
		y = 0.0;
		xs = -2.5 + i / 100.0;
		ys = -2.5 + j / 100.0;
		k = 0;
		do
		{
			xnew = x*x-y*y + xs;
			ynew = 2.0*x*y + ys;
			x = xnew;
			y = ynew;
			k++;
		} while (x*x + y*y ≤ 6.25 && k ≤ kmax);
		PlotPixel(i, j, color);
	}
}
Mandelbrot Tile Variant #1 with Pseudocode
for (int i = 0; i ≤ 500; i++)
{
	for (int j = 0; j ≤ 500; j++)
	{
		x = 0.0;
		y = 0.0;
		xs = -2.5 + i / scale;			
		ys = -2.5 + j / scale;
		k = 0;
		do
		{
			xnew = x*x-y*y + cos(xs) - sin(ys);
			ynew = 2.0*x*y - cos(xs) - sin(ys);
			x = xnew;
			y = ynew;
			k++;
		} while (x*x+y*y ≤ 6.25 && k ≤ kmax);
		PlotPixel(i, j, color);
	}
}
c02.jpg
Mandelbrot Build: (f(x,y), g(x,y)) Escape: h(x,y)>value Tile Generator Scale
Basic Mandelbrot Set (x² - y², 2.0*x*y) x² + y² > 6.25 None None
Mandelbrot Tile Variant #1 (x² - y², 2.0*x*y) x² + y² > 6.25 (cos(xs)-sin(ys), -cos(xs)-sin(ys)) 50.0
Mandelbrot Tile Variant #2 (x² - y², -2.0*x*y) x² + y² > 6.25 (cos(xs)-sin(ys), -cos(xs)-sin(ys)) 50.0
Mandelbrot Tile Variant #3 (x² - y², 2.0*x*y) x² + y² > 6.25 (-cos(xs), -sin(ys)) 50.0
Mandelbrot Tile Variant #4 (x*y*y, x*x*y) x² + y² > 6.25 (-cos(xs), -sin(ys)) 50.0
c01.jpg c02.jpg
Julia Set with Pseudocode
for (int i = 0; i ≤ 500; i++)
{
	for (int j = 0; j ≤ 500; j++)
	{
		xs = 0.0;
		ys = 0.0;
		x = -2.5 + i / 100.0;
		y = -2.5 + j / 100.0;
		k = 0;
		do
		{
			xnew = x*x-y*y + xs;
			ynew = 2.0*x*y + ys;
			x = xnew;
			y = ynew;
			k++;
		} while (x*x + y*y ≤ 6.25 && k ≤ kmax);
		PlotPixel(i, j, color);
	}
}
Julia Tile Variant #1 with Pseudocode
for (int i = 0; i ≤ 500; i++)
{
	for (int j = 0; j ≤ 500; j++)
	{
		xs = 0.234;
		ys = 0.82;
		x = -2.5 + i / scale;
		y = -2.5 + j / scale;
		k = 0;
		do
		{
			xnew = cos(x)*cos(x)-cos(y)*cos(y) + xs;
			ynew = 2.0*cos(x)*sin(y) + ys;
			x = xnew;
			y = ynew;
			k++;
		} while (x*x+y*y ≤ 6.25 && k ≤ kmax);
		PlotPixel(i, j, color);
	}
}
c02.jpg
Julia Build: (f(x,y), g(x,y), (xs,ys)) Escape: h(x,y)>value Scale
Basic Julia Set (x² - y², 2.0*x*y), (0.0, 0.0) x² + y² > 6.25 None
Julia Tile Variant #1 (cos(x)²-cos(y)², 2.0*cos(x)*sin(y)), (0.234, 0.82) x² + y² > 6.25 50.0
Julia Tile Variant #2 (cos(x)*sin(x)*sin(y), sin(y)*cos(x)*cos(x)), (1.327, 1.777) x² + y² > 6.25 50.0
Julia Tile Variant #3 (sin(y)*sin(y)+sin(x), sin(y)*cos(x)), (1.1415927, 0.445386) x² + y² > 6.25 50.0
Julia Tile Variant #4 (sin(y)*sin(y)+sin(x), cos(y)*cos(x)), (1.1415927, 0.445386) x² + y² > 6.25 50.0