Why are chaotic attractors infinitely complex?

About the author

Hey all,

I am George Datseris, currently a postdoctoral researcher at the Max Planck Institute for Meteorology. Nonlinear dynamics has been my field of expertise for the last 6 years or so, and remains my prime scientific interest. I am most passionate about education and accessibility of science, and specifically nonlinear dynamics. I have been active in teaching nonlinear dynamics for the last 5 years, and recently published a textbook on the topic, called Nonlinear Dynamics: An introduction interlaced with code. I've spent much of my free time developing a scientific software organization for nonlinear dynamics and complex systems called JuliaDynamics.

Last summer I participated in SoME1. My video about explaining the butterfly effect by using billiards made it to the top 100 of the competition, although I don't this ranking matters that much. The animation content of this video was made by using a library I've developed called InteractiveDynamics.

Quick Summary

Already since last November I had an idea for the topic I wanted to do for SoME2. Unfortunately, I realized I would not be able to participate this summer because I need to spent my time writing grant applications (science life is tough). So I was absolutely delighted to see that Grant and James have set up this collaboration possibility, because at least from my perspective, the technical aspects of making the video took the majority of my time.

My idea for the current topic is a continuation of the previous video of what is the nature of the butterfly effect. This time, I suggest to discuss more the "geometry" of these weird objects that trajectories form in the state space, called "strange attractors". Example image:

(from https://discourse.mcneel.com/t/strange-attractors/120053 )

These objects are infinitely complex. But why? (by the way my plan is that this question and a chaotic attractor form the thumbnail of the video). (To clarify, the catchy name "infinitely complex" actual means the more established term "fractal")

It turns out that it is possible to justify why these objects have to be infinitely complex, although it does rely a tiny bit on having a basic idea of chaos and the "sensitive dependence on initial conditions" that I've explained in my first SoME1 video. So I guess this should be refreshed briefly in a couple of minutes. The video will also then be educating about fractals in general, what makes them interesting, and what are their key properties that actually connect them with deterministic chaos. Let me know if you'd need any other info or background, I'm happy to answer any question besides the actual answer to the title question (I'd rather not spoil the surprise in this public setting but will of course convey all of my knowledge in detail to the potential collaborators).

The target audience is similar to the target audience of the first video: humans interested in dynamical systems / nonlinear dynamics / chaos / fractals / sensitive dependence on initial conditions and all these fun stuff. Similarly to the first video, my idea is to explicitly showcase mathematical concepts, but they will be introduced appropriately slowly an in sufficient detail, so that they are accessible by a general audience.

Target medium

Video or interactive article. The animations I've used in my first video are actually from interactive GUIs that I simply recorded into .mp4. The skillsets I am looking for in the collaborator are composition, pacing, video editing, animation production, voice over or voice over instructions/coaching (I am happy to use my voice, but my first video was really bad as narration goes. Even though in lectures I am full of life and inspiring the students, turns out in a pre-recorded format I suck).

Given that I have developed software that can make all these nice animations of chaotic attractors in Julia out of the box, it would be to the benefit of the collaborator to have a basic handling of Julia and InteractiveDynamics.jl and the Makie plotting ecosystem.

More details

I have a rough outline in mind, but given that one of the major points of improvement compared to my previous effort needs to be pacing, it is best to discuss an outline with the collaborator first.

I guess best textbook reference for answering the topic's question would be Kantz & Schreiber "nonlinear time series analysis", chapter 11.

For learning more about fractals I'd recommend chapter 5 of my book and I can answer any questions you might have on fractals on this Issue Thread.

Contact details

Reply to this topic, or via email (linked in my GitHub account).

leios / SoME_Topics