sup

That's what you do, isn't it?

I see what you did there.

Sometimes the only solution is to find a new problem.

Black hole?

Black hole?

If enough paths are drawn, it will be. In general (in the mathematical sense of "in every case", not "usually"), all paths cover every point in the plane, and no two paths ever intersect.

Anyway, I didn't find any graphing programs for general systems of ordinary differential equations that would draw more than a small number of (usually unsymmetrical) paths. Since ODEs are pretty cool, I decided to start writing one.

The "black hole" system is described by




A few additional ones that I thought turned out pretty well:









Some lines are broken because it only plots systems in unidirectional time, for now.

Also, the odd helix-shape in the last image is due to a (very small) time dependency, which I didn't introduce into any of the other systems. The greater the time dependency, the more chaotic paths around the stationary point in the vortex become.

Time dependency in ODEs tends to make organized paths "fall apart", which is a kind of neat example of how time and entropy are strongly related, I think.

A 3D projection of a tesseract projected on a 2D plane is always relevant.

which is producing a 1 dimensional shadow

tesseract ftw

Reminds me of this: http://www.spacetimetravel.org/wurml...mlochflug.html
This wormhole model (the photon path equations) is implemented in real time in EvE, excepting that you cannot pass though the threshold without triggering a session change. Skimming the threshold is probbably the trippiest thing I've ever seen.

Reminds me of this: http://www.spacetimetravel.org/wurml...mlochflug.html This wormhole model (the photon path equations) is implemented in real time in EvE, excepting that you cannot pass though the threshold without triggering a session change. Skimming the threshold is probbably the trippiest thing I've ever seen.

Need video.