Logo Contest: JuliaDynamics (also "announcement")

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Hi all,

After a lot of time thinking whether to join some existing packages with some other existing organizations or create a new, I’ve made a new one called “JuliaDynamics”: JuliaDynamics · GitHub. So far it only has 2 packages, DynamicalSystems.jl and DynamicalBilliards.jl, both with a significant amount of content.

I hope more people find themselves interested in this and would like to join and/or create collaborations. In my personal opinion, I think organizations are very useful not only for coding collaboration but also for grouping similar thematic content. I really hope that more people share this opinion, because for me it has been useful so far.

With this I would gladly invite any package that feels like it has similar content to the ones existing already in the organization, or to what the name of the organization stands for. Many have suggested that general packages that are aimed in simulations would fit here, like for example Sims.jl from @tshort and many more.

EDIT: Added gitter channel: https://gitter.im/JuliaDynamics/Lobby

Logo contest:

Okay, the logo that I have so far for the organization is this:
logo_billiard

it’s actually stolen from the homepage of DynamicalBilliards :smiley:

I was thinking a lot about what kind of logo I could use for either this organization page or even the package DynamicalSystems.jl and after some tries with @cormullion I’m making this post to invite others if they want to tackle it! A previous post on the site about the logo of JuliaPhysics seemed to be enjoyed very much by the community!

Other ideas I had about the logo is to use the fractal attractor basin of the three magnet pendulum, which looks like:
magpendattractor
(of course replacing the colors with the julia colors - if somebody can do that please go ahead!).

Another good idea is to create a system with 3 attractors, much like the magnet one but much more regular, and make each attractor be one of the 3 julia balls. Something like this:
screenshot
but with 3 attractors instead.

Well, the rest is up to you! Also, if you think you know anybody interested in the organization, go ahead and tag them. I will be glad to do modifications to some of my code to be able to interact with other codes, if something like this is advantageous.

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Why not a Julia set? Like e.g.,
https://de.wikipedia.org/wiki/Benutzer:Georg-Johann/Mathematik#/media/File:Julia-set_N_z3-1.png

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I wonder how come I never thought about that…

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The Julia set looks like a good source of images. Is it the same as in the JuliaMath org logo?

JuliaMath

I love the cool images that you can get with dynamic systems, strange attractors, chaos, Poincare sections, fractals. Although, for logos, you often want something simple, distinctive, and versatile; sometimes you only have 128 by 128 pixels to work with, and all those fractal details might be washed away through the pixel grid.

It would be quite cool to have a dynamic logo, one that changes all the time. (It’s not that unusual. The Mathematical Museum and the MIT Media Lab are recent examples. Perhaps they just couldn’t make up their minds…! Could you hack GitHub to show a different logo each time…? :slight_smile:

I investigated the chaotic double pendulum idea briefly. While it’s fun while moving, it’s less interesting when it’s stationary… Or perhaps it could leave a trail…

pendulums

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The issue with the gif is that if you make it loop nicely it won’t be chaotic any more :slight_smile:

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Although it should be by definition impossible to be able to make it loop properly (without cuts), Mike is right. But still it looks damn cool!

But I think the idea of the trail is wonderful! (with a white background). The only concern would be the size. Since the julia-balls have to take up a significant portion of the logo, the trail will be mostly out of the rectangle. On the other hand, if most of the trail is inside the rectangle, the balls will be very small…? Maybe @cormullion can do some magic so that it looks cool :smiley:

Nobody likes the idea of the fractal basin of attraction of the magnetic pendulum that I posted I guess…?

p.s. daaaaamn the math museum logo is really nice idea! I wish it was possible to have a moving logo on github. But @cormullion do not forget, I still need something to use for the page of the package DynamicalSystems.jl and there, there is absolutely no problem with moving gifs!!!

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pendulums

It only looks chaotic the first time you watch it…

(Sorry for uploading these large-ish GIFs…)

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Recolored basin:

luxor-drawing

It’s a bit, Austin Powers… :slight_smile: Groovy.

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“Groovy” hahaha

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Okay!!! After months, I am finally presenting the final logo:

Systems_logo_animated_optimized
Systems_logo_animated_optimized882×300 2.27 MB

This is the animated version.
Now, for the icon of the julia organization, I want to choose one of the two following frames:
Notice: I will only choose the pendulum part of the frames. I am posting them like this because I was too lazy to seperate them
Frame 1:
logosug1
logosug1882×300 72 KB

Frame 2:
logosug2
logosug2882×300 73 KB

Both of these frames have the pendulum close to the julia 3-balls and they got a nice big spread in the pendulum trajectory.

What do you think?

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The logos are amazing. Especially the animated version, it is mesmerizing.

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Nice work! Frame 1 registers slightly better when small, perhaps…

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Yeah, I went with frame 1 after testing it on github.

If you see the logo next to the org here: https://github.com/JuliaDynamics it looks suprising good and detailed. I was expecting the “orbit trace” to be almost invisible but fortunately for me it was not the case!

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It would be an unstable periodic orbit. Those are very significant in dynamical system theory. Unstable periodic orbits - Scholarpedia

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Do you have code for calculating unstable periodic orbits of ODEs in julia? That would be very nice!

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Unfortunately no, not yet…

However, it is definitely coming soon! You see, I have already used this method in research; in fact, I used it in my first published paper (and only one so far :D). One of the “creators” of the method described here (F. Diakonos) was my first supervisor.

So, you have to be a bit patient! Right now I am implementing the method to calculate lyapunov exponents from measured timeseries (without having dynamical equations)

EDIT: I now realise you were talking about continuous systems. Soooorry I don’t have that and I also don’t know how to do it… So you have to find somebody to contribute it!

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No, mine is in C++ and geared toward very-high-dimensional systems like fluid simulations. For ODEs, I think it would be a matter of coordinating DifferentialEquations.jl with the nonlinear solvers in NLsolve.jl, plus some relatively simple preprocessing code to generate good intial guesses from time series of ODE integrations. That would be a fine project for someone. I have a couple undergrads hankering for research projects; maybe they’d be able.

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Do you have a resource which discusses this? I am curious because I’ve never looked into methods for numerically finding unstable periodic orbits. My first instinct would be to reverse the integration and then using that to find the periodic orbit in the reversed problem. Or from here:

http://www.scholarpedia.org/article/Periodic_orbit

it looks like we can make use of the BVP solvers.

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This paper by Diivakar Viswanath (U Michigan) describes how to coordinate PDE time-integration, Krylov subspace methods, and trust-region Newton methods to find unstable periodic orbits in closed, weakly turbulent flows. I’ve implemented the algorithm in C++ and have a good amount of experience in computing unstable periodic orbits in plane Couette and channel flow. My source code comments (end of file) are a bit more of a unified presentation of all the elements of the algorithm than Viswanath’s paper.

But for ODEs, you can replace the Krylov methods with straightforward direct Ax=b solves, and the whole thing becomes a lot easier. Essentially you do a trust-region Newton method over (x,T) to solve f^T(x) - x = 0 where f^t is time-t forward-time integration of the ODE and x is the state space. Some care is required to interpolate or otherwise adjust the time step to fit the interval T that changes during the search.

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You can’t just reverse the integration because the directions that are stable in forward time are unstable in backwards time. BVP solvers should be a good solution.

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