CHAPTER 2
Tile Variations
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); } }
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 |
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); } }
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 |