Lorenz Attractor Simulation

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Animated 3D illustration of the Lorenz Attractor, modeled with five thousand spheres. The positions of the spheres represent the iterates of the Lorenz equations. The color changes from cool blue to warm orange by iteration count.
A frame from this video was contributed to illustrate the article "Chaos at fifty" by Adilson E. Motter and David K. Campbell in "Physics Today", May 2013.
The music - "Hungarian Dance No. 6 In D Major" by Johannes Brahms, Philharmonia Cassovia, audio swap from RU-vid.
Equations:
dx/dt = Sigma (y - x); dy/dt = x (Rho - z) - y; dz/dt = xy - Beta z
Parameters:
Sigma=10, Rho=28, Beta=8/3.
Coded with Microsoft Visual C++, OpenGL rendering using Cinder (libcinder.org).

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Опубликовано:

5 апр 2011

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Комментарии : 43

@posslart 12 лет назад

the audio syncs up almost perfectly with the movement, it's really quite something!

@JimBCameron 10 лет назад

I've always found Lorenz Attractors beautiful images, but it wasn't until I understood what it's a graphical representation of that I really started to properly appreciate it's beauty! :D

@thewhatever379only 11 лет назад

my hat off to you good sir. You have just done a REMARKABLE demonstration on the beauty of mathematics.

@calpapichulo 11 лет назад

Awesome! Please post more!

@StefanGanev 12 лет назад

Thank you for your kind comment! I am glad you enjoyed it.

@MountainManBN 12 лет назад

amazing video! thank you for your efforts in sharing this incredible work.

@zed0kun 11 лет назад

I'm not that far into the maths yet, but If anything, this looks like two galaxies colliding. Awesome.

@mixedartmaster 12 лет назад

Nice work!

@McGuireMechanism 11 лет назад

Great work

@StefanGanev 12 лет назад

@ApolloCobain Thanks; glad you enjoyed it!

@StefanGanev 12 лет назад

@semitrailer27 The color gradient is from cool blue to warm red hue. No green spheres. A moderate amount of constant green component is there to keep the blue and red from becoming over-saturated. Thanks for your interest!

@StefanGanev 11 лет назад

Thank you, you are very kind!

@printz150 11 лет назад

Awesome, I'm looking up this Cinder SDK now :D

@StefanGanev 11 лет назад

In reply to why Euler: good point, and interesting one, because the sensitive dependence on the initial condition also means sensitive dependence on the computational error (or accuracy). In a more recent implementation I used RK4 (4th-order Runge-Kutta) as well. It is interesting to observe how the accuracy of the method affects the result after some number of steps. Sensitivity can be observed even when switching between double vs. single precision floating point calculations alone.

@StefanGanev 11 лет назад

Thank you for your feedback. I will probably add a few references to address that.

@bapaden 12 лет назад

Love it! Deserves more views

@irchristo 11 лет назад

Wonderful...!

@MaitredeDieu 12 лет назад

i agree, music and video works weedy well together ! great job on that for a moment, i felt like wandering through space like in 2001, space odd. :D

@StefanGanev 12 лет назад

@MrOrches I used low number of stacks and slices (~10 or less) during development to get it running mostly real time on my system with modest GPU. Some high-end GPUs would probably handle significantly more in real time. For the final rendering it was something in the range between 25-30 stacks and slices. The number of vertices is like stacks x slices x 6 for each sphere, implemented in Cinder as one gl::VboMesh for the whole set of spheres. Thanks for your question.

@NerdyBeautyX0X0 11 лет назад

3 people couldn't wrap their minds around this beauty

@pjhirsch 11 лет назад

Physics Today, May 2013, has an explanation -- and links to this video. The article is "free," not behind the subscription firewall.

@erzetic 12 лет назад

Excellent

@StefanGanev 12 лет назад

@semitrailer27 Yes, it is a model based on the famous Lorenz equations.

@StefanGanev 11 лет назад

Thank you!

@kitemanmusic 12 лет назад

Very nice Video. This reminds me of the work of Philip Latham, and his programme Organic Art. I have got my copy to work on Windows XP

@StefanGanev 11 лет назад

Thanks a lot for your comment!

@dedly13 11 лет назад

the two wings are analogous to two different directions of a waterwheel spinning with little buckets being filled at the top of the wheel with little holes in each one, there is a good book on this called chaos

@semitrailer27 12 лет назад

Lorenz of chaos theory investigation, yes?

@alreadytakenthe3rd 12 лет назад

What's the music?

@StefanGanev 12 лет назад

@MaitredeDieu Thanks a lot for your so kind comment!

@StefanGanev 12 лет назад

@Greynaide Thank you, appreciate your comment!

@StefanGanev 12 лет назад

"Hungarian Dance No. 6 In D Major" by Johannes Brahms - Philharmonia Cassovia, Andrew Mogrelia

@StefanGanev 12 лет назад

@bapaden - thank you!

@StefanGanev 12 лет назад

@gogginfilms Thanks!

@semitrailer27 12 лет назад

do you have any green spheres?

@josephgarretsullivan4762 11 лет назад

Why did you choose to use Euler step? Ease of computation? I suppose it makes no difference for the purposes of illustrating the beauty of this system, but certainly there are much more accurate methods!