FRACTAL FIND
APPENDIX C
Unit Circle Variation Balls
The case could be made that this is not a true Julia set unit circle variation. Quibble if you choose, but enjoy the figures.
Each figure builds dynamically.
- xa = fa(θ)
- ya = ga(θ)
- xb = fb(θ)
- yb = gb(θ)
- mmin ≤ m ≤ mmax
- scale = scalea, scaleb
- point = ((scalea*xa + scaleb*xb*m),(scalea*ya + scaleb*yb*m))
Unit Circle with Pseudocode
Unit Circle
Example Ball
Example Ball
for (θ = 0; θ ≤ 360000; θ++)
{
xnew = cos(θ);
ynew = sin(θ);
x = 0.0;
y = 0.0;
for (m = 0; m ≤ 0; m++)
PlotPoint(200.0*xnew+1.0*m*x, 200.0*ynew+1.0*m*y, color);
}
Example Ball with Pseudocode
for (θ = 0; θ ≤ 1800000; θ++)
{
xnew = cos(0.4001*θ);
ynew = sin(0.4001*θ);
x = cos(θ);
y = sin(θ);
for (m = 0; m ≤ 19; m++)
PlotPoint(200.0*xnew+4.0*m*x, 200.0*ynew+4.0*m*y, color);
}
| Ball | Build: (fa(θ),ga(θ))(fb(θ),gb(θ)) | Scale: scalea, scaleb | Offset: mmin, mmax |
|---|---|---|---|
| Unit Circle | (cos(θ),sin(θ))(0.0, 0.0) | 200.0, 1.0 | 0, 0 |
| Example | (cos(0.4001*θ),sin(0.4001*θ))(cos(θ),sin(θ)) | 200.0, 4.0 | 0, 19 |
| Ball #1 | (cos(0.1101*θ)*sin(0.01*θ),sin(0.1101*θ)*sin(0.01*θ))(cos(0.1101*θ)*sin(0.01*θ),sin(0.1101*θ)*sin(0.01*θ)) | 375.0, 0.0 | 0, 51 |
| Ball #2 | (cos(0.99*θ)*sin(0.02*θ),sin(0.99*θ)*sin(0.02*θ))(cos(0.99*θ)*sin(0.02*θ),sin(0.99*θ)*sin(0.02*θ)) | 375.0, 0.0 | 0, 51 |
| Ball #3 | (cos(0.999*θ)*sin(0.0025*θ),sin(0.999*θ)*sin(0.0025*θ))(cos(0.999*θ)*sin(0.0025*θ),sin(0.999*θ)*sin(0.0025*θ) | 225.0, 0.0 | 0, 51 |
| Ball #4 | (cos(0.9*θ)*sin(0.9999*θ),sin(0.9*θ)*sin(0.9999*θ))(cos(0.9*θ)*sin(0.9999*θ),sin(0.9*θ)*sin(0.9999*θ)) | 375.0, 0.0 | 0, 0 |
| Ball #5 | (cos(θ),sin(θ))(cos(0.001*θ),sin(0.001*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #6 | (cos(0.301*θ)*sin(0.302*θ),sin(0.301*θ))(cos(0.301*θ)*sin(0.302*θ),sin(0.301*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #7 | (cos(0.5*θ)*sin(0.301*θ),sin(0.5*θ)*cos(0.301*θ))(cos(0.5*θ)*sin(0.301*θ),sin(0.5*θ)*cos(0.301*θ)) | 225.0, 3.0 | 0, 51 |
| Ball #8 | (cos(0.998*θ)*tan(0.998*θ),cos(0.998*θ)*cos(0.999*θ))(cos(0.998*θ)*tan(0.998*θ),cos(0.998*θ)*cos(0.999*θ)) | 225.0, 3.0 | 0, 51 |
| Ball #9 | (cos(0.081*θ)*tan(0.081*θ),cos(0.081*θ)*cos(0.080*θ))(cos(0.081*θ)*tan(0.081*θ),cos(0.081*θ)*cos(0.080*θ)) | 225.0, 3.0 | 0, 51 |
| Ball #10 | (cos(θ),sin(θ))(cos(0.0001*θ)*tan(0.0001*θ)-sin(0.008*θ)*sin(0.008*θ))(2.0*cos(0.0001*θ)*sin(0.008*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #11 | (cos(θ),sin(θ))(cos(0.001*θ)*tan(0.001*θ)-sin(0.001*θ)*sin(0.001*θ),2.0*cos(0.001*θ)*sin(0.001*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #12 | (cos(θ),sin(θ))(cos(-0.99*θ)*tan(-0.99*θ)-sin(-0.99*θ)*sin(-0.99*θ),2.0*cos(-0.99*θ)*sin(-0.99*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #13 | (cos(θ),sin(θ))(cos(-0.501*θ)*tan(-0.501*θ)-sin(-0.501*θ)*sin(-0.501*θ),2.0*cos(-0.501*θ)*sin(-0.501*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #14 | (cos(θ),sin(θ))(cos(0.01*θ)*cos(0.01*θ)-sin(-0.994*θ)*sin(-0.994*θ),2.0*cos(0.01*θ)*sin(-0.994*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #15 | (cos(θ),sin(θ))(cos(-θ)*cos(-θ)-sin(-θ)*sin(-θ),2.0*cos(-θ)*sin(-θ)) | 200.0, 3.0 | 0, 51 |
| Ball #16 | (cos(θ),sin(θ))(cos(1.005*θ),sin(1.005*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #17 | (cos(θ),sin(θ))(cos(-1.01*θ),-sin(-1.01*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #18 | (cos(θ),sin(θ))(cos(-0.5*θ),sin(-0.5*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #19 | (cos(θ),sin(θ)(cos(-1.1*θ),sin(-1.01*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #20 | (cos(θ),sin(θ))(cos(-0.7503*θ),sin(0.5*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #21 | (cos(θ),sin(θ))(cos(-0.8001*θ),sin(-0.8001*θ) | 200.0, 3.0 | 0, 51 |
| Ball #22 | (cos(θ),sin(θ))(cos(-0.75*θ),sin(0.375*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #23 | (cos(-0.7503*θ),sin(0.5*θ))(cos(θ),sin(θ)) | 200.0, 3.0 | 0, 51 |
| Ball #24 | (cos(-0.2*θ),sin(0.75*θ))(cos(θ),sin(θ)) | 200.0, 3.0 | 0, 51 |
