Celestia Forums

Just for the fun of it, I made this Lorenz attractor in CMOD format. Kinda pretty, in 3D !





That curve has 5000 points. It's a 356KB CMOD file, in ASCII.

I tried to use a .xyz version of it, and make a spaceship following that path (and for my trapped particles in Earth's magnetic field), but it doesn't work, I don't know why. O well ...

Did Escher come up with that?! What IS it? And what's it supposed to "attract"?

It's a famous mathematical object in chaos theory, the origin of the well known "butterfly effect" celebrity (it looks like a butterfly). It's an attractor in the sense that any initial condition will goes to the same cahotic final state.

EDIT :

Selden : sorry, this topic should belong to purgatory. It has nothing to do with real "addons". Please, move it there, where it belong.

If someone want to play with this strange mathematical object, here's a link to the addon :

http://nho.ohn.free.fr/celestia/Cham/Lorenz.zip

Well, obviously this is a real addon now

Celestia is quite usable for general-purpose 3D visualization if the appropriate model generation tools are available.

Progress on the CELX/Lua front would seem to suggest that realtime creation of graphics may be available in the not too distant future, too.

http://mathworld.wolfram.com/LorenzAttractor.html

Just in case someone still doesn't know what a Lorentz attractor is and where it appears...

Bye Fridger

t00fri wrote:http://mathworld.wolfram.com/LorenzAttractor.html

Yeah, it is beautiful

Cham wrote:It's a famous mathematical object in chaos theory, the origin of the well known "butterfly effect" celebrity (it looks like a butterfly).

No, the "butterfly effect" refers to extreme sensitivity to initial conditions in any chaotic system. The term comes from the notion that a butterfly flapping its wings in China can cause a hurricane in the Gulf of Mexico. It does apply to the Lorenz attractor, in that the curves starting from two infinitesimally different sets of initial conditions follow increasingly divergent shapes over time, but the name has nothing to do with the shape of the attractor.

I'm well aware of this stuff, but you are probably right that the name isn't related to the shape of the Lorenz attractor. The name's origin (not the principle) was an interpretation from myself.

Christopher wrote:

Cham wrote:It's a famous mathematical object in chaos theory, the origin of the well known "butterfly effect" celebrity (it looks like a butterfly).

No, the "butterfly effect" refers to extreme sensitivity to initial conditions in any chaotic system. The term comes from the notion that a butterfly flapping its wings in China can cause a hurricane in the Gulf of Mexico. It does apply to the Lorenz attractor, in that the curves starting from two infinitesimally different sets of initial conditions follow increasingly divergent shapes over time, but the name has nothing to do with the shape of the attractor.

That's certainly correct. The "Butterfly Effect", or more technically the "sensitive dependence on initial conditions", is the essence of chaos. The Butterfly shape of the Lorentz attractor and the "Butterfly effect" are two different issues in the same field (chaos)

Bye Fridger