sup

[Chruser]

I... I...

http://zelaron.com/apax/Symm.png

I thought you were a GEP gun.

[Grav]

This is surprisingly arousing

[Chruser]

Let's visit the multiverse.

http://zelaron.com/apax/q.png

[Chruser]

Let's visit the multiverse.


Oh my God — It's full of stars!

http://zelaron.com/apax/RRLL.png

[KagomJack]

Our fearless leader returns!

[Boomerang]

I, too, have returned.

[KagomJack]

I don't know you.

[Sovereign]

Aahaha. You sat on a scanner and took an image of your ass then added color didn't you

[!King_Amazon!]

I, too, have returned.
Boomerang=Skurai

[Skurai]

Oh my God — It's full of stars!

http://zelaron.com/apax/RRLL.png

Is that a butt? lol

[-Spector-]

You're all faggots.

[Skurai]

And you're the king of us. The king of all faggots.

[Chruser]

Aahaha. You sat on a scanner and took an image of your ass then added color didn't you


No, but interestingly, that's how the Mandelbrot set was originally created.


I, too, have returned.


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

[HandOfHeaven]

That might be correct.

[Skurai]

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

I see what you did there.

[Chruser]

Sometimes the only solution is to find a new problem.

http://zelaron.com/apax/TVEQ.png

[Asamin]

Black hole?

[Chruser]

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


\begin{cases}
\frac{dx}{dt} = -y + x (1-x^2-y^2)\\
\frac{dy}{dt} = x + y (1-x^2-y^2)
\end{cases}



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

http://zelaron.com/apax/GlassOfTemporality.png

http://zelaron.com/apax/Alienoid.png

http://zelaron.com/apax/Ordinaire.png

http://zelaron.com/apax/TimeVortex.png

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.

[Sum Yung Guy]

http://upload.wikimedia.org/wikipedia/commons/5/55/8-cell-simple.gif

[Chruser]

http://upload.wikimedia.org/wikipedia/commons/5/55/8-cell-simple.gif


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

[Sum Yung Guy]

which is producing a 1 dimensional shadow

[-Spector-]

tesseract ftw

[Asamin]

I'm currently taking differential Equations. Those pictures make it more appealing.

[Sum Yung Guy]

http://i.imgur.com/BWFzo.jpg

[!King_Amazon!]

http://i.imgur.com/BWFzo.jpg
http://i0.kym-cdn.com/photos/images/original/000/024/183/500pxShopped.jpg?1318992465

[Sum Yung Guy]

ill kill u nigger

[kaos]

http://www.deviantart.com/download/148394314/Shopped_or_no__by_Keilight.jpg

[WetWired]

Reminds me of this: http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.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.

[!King_Amazon!]

Reminds me of this: http://www.spacetimetravel.org/wurmlochflug/wurmlochflug.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.

[WetWired]

Sorry, no fraps here.

[Asamin]

L2Youtube
9_KrXo6z0Hk&feature=fvst

[WetWired]

He never does what I was talking about.

[WetWired]

This isn't really what I was talking about either. This is the only wormhole I could find on short notice, but it's disturbed (the pulsating effect you see), and it isn't large enough for me to orbit it at the threshold. Never the less, I thought you might like it. Maybe next time I find the right one, I'll remember to make a video.
http://wwuzone.com/bitbin/wh.wmv

The effect I wanted to show was the extreme distortion of space on both sides, but you can't really see this through the pulsing.

[!King_Amazon!]

Pretty cool regardless.

[Chruser]

Bump. I never posted my Java implementation of the generalized version of Langton's Ant (http://en.wikipedia.org/wiki/Langton%27s_ant) (that I use a variation of for my browser-breaking signature), so here it is:

http://zelaron.com/apax/Langton.html

Refresh your browser a few times if you're bored. It takes maybe 15 attempts on average to get something particularly interesting.

Relatively short rules tend to result in interesting geometric patterns, like this (whereas long ones tend to produce smooth hue gradients):

http://zelaron.com/apax/pyr.png


Take a screenshot of your findings and post them!