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))
Example Ball
for (θ = 0; θ ≤ 36000; θ++)
{
xnew = cos(0.01*θ);
ynew = sin(0.01*θ);
PlotPoint(100.0*xnew, 100.0*ynew, 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(0.01*θ),sin(0.01*θ))(0.0, 0.0) | 100.0, None | None, None |
| 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))(0.0, 0.0) | 300.0, None | None, None |
| Ball #2 | (cos(0.99*θ)*sin(0.02*θ),sin(0.99*θ)*sin(0.02*θ))(0.0, 0.0) | 300.0, None | None, None |
| Ball #3 | (cos(0.999*θ)*sin(0.0025*θ),sin(0.999*θ)*sin(0.0025*θ))(0.0, 0.0) | 300.0, None | None, None |
| Ball #4 | (cos(0.9*θ)*sin(0.9999*θ),sin(0.9*θ)*sin(0.9999*θ))(0.0, 0.0) | 300.0, None | None, None |
| Ball #5 | (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 #6 | (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)) | 200.0, 3.0 | 0, 51 |
| Ball #7 | (cos(0.08*θ)*sin(0.998*θ),cos(0.999*θ))(cos(0.08*θ)*sin(0.998*θ),cos(0.999*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #8 | (cos(θ),sin(θ))(cos(-0.301*θ)*sin(-0.501*θ)-sin(-0.501*θ)*sin(-0.301*θ),2.0*cos(-0.501*θ)*sin(-0.501*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #9 | (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 #10 | (cos(θ),sin(θ))(cos(-1.01*θ),-sin(-1.01*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #11 | (cos(θ),sin(θ))(cos(-0.5*θ),sin(-0.5*θ)) | 200.0, 3.0 | 0, 51 |
| Ball #12 | (cos(θ),sin(θ))(cos(-0.8001*θ),sin(-0.8001*θ) | 200.0, 3.0 | 0, 51 |
