|
-
|
||
|
-
|
(local copy) <--- since the Geometry Centre is now closed. | |
|
The secret to fast convergence is choosing a (relatively) large timestep, but then the unstable manifold of the origin expands too fast. To get around this we use about a thousand test points per cube! Compare the 3 images below to those further down the page where either the origin is not included or the "fold" of the attractor is far from convergance.
---------- Stuff below this line is from the original work on the project. ---------- Animations
Images |
|||||||||||||
|
Images which appear in the project
report.
|
|||||||||||||
|
Posters.
|
||||||||||||
|
Lorenz global attractor images.
|
||||||||||||
 |
Convergence of the algorithm.
|
||||||||||||
 |
How the choice of time step affects the approximation.
|
||||||||||||
  |
Extrapolating the Fractal dimension. | ||||||||||||
The images below are from an earlier stage of the project. They use a time step which is slightly too small to resolve the unstable manifold of the origin. The effects of which are illustrated in the above diagram. However they illustrate the general shape of the global attractor more clearly, because of the faster convergence elsewhere.
 3D view |
|
 3D view |
 3D view |
 3D view |
 A "relative" global attractor |
 Unstable manifold of origin |
 X vs Y projection |
 X vs Z projection |
 Y vs Z projection |
 Plastic wrapped image |
 Plastic wrapped image |
Plastic wrapped image |
 Plastic wrapped image |
|
|
|