FRACTAL FIND
Explore Fractal and Quantum Variations
Lynn Wienck
APPENDIX H
Line Variations
Line Variations use modified Mandelbrot configurations with pixels plotted at iteration count increment.
See Appendix D for similar Mandelbrot Tile Variations.
xnew = f(x, y)
ynew = g(x, y)
escape = h(x, y, k)
k = iteration count
Example Lines with Pseudocode
Computer-generated outline {pseudocode)
Computer-generated colors (no 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 = k + 1;
xnew = -x * x * y * y + xs;
ynew = y * x * x + ys;
x = xnew;
y = ynew;
} while ((k ≤ kmax) && (|x|+|y| ≤ 16.0/k));
if (k != oldk) 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 = k + 1;
xnew = -x * x * y * y + xs;
ynew = y * x * x + ys;
x = xnew;
y = ynew;
} while ((k ≤ kmax) && (|x|+|y| ≤ 16.0/k));
if (k != oldk) PlotPixel(i, j, color);
oldk = k;
}
}
FRACTAL FIND
Computer-generated colors (no pseudocode)
