Lorenz Distractors: Rainbow Variant + 4K Wallpaper
I've seen a lot of references to the concept of the Lorenz Attractor recently, but one execution of the idea really stood out from all the others - the image used in the Animation Nodes v1.6 release announcement. Doubly inspired because Animation Nodes is one of my favorite tools of all time, I -had- to learn not only the techniques used to create such a beautiful flow of curves, but also the math behind the system. So I dove in - but I got distracted while working on it, and this is what I created instead of a faithful reproduction of the system.
Higher resolution + Wallpaper:
https://goo.gl/photos/j2rGFzTzzHqFKS3YA
When I got started, I became aware of the existence of the related concepts of "Strange Attractor", "Phase Space", and "Phase Portrait". I started with reading WikiPedia articles on the topics, and when the math got too dense with Greek symbols for my ability to understand, I turned to YouTube. Then when the video lectures became too dry for my ability to focus, I decided to just start building an Animation Nodes setup based on what I already knew about the equation - and before I got to anything remotely resembling a reliable reproduction of the idea, the output in my scene was already beautiful. So I kept moving down the path of beautiful distraction, and this is where it ended up - another design I'm happy to have completed. My rate of ideas that make it through to completion has been 1/6th lately, so every design that gets this far feels like a major victory in my struggle to produce new work. I will have to revisit many of the original concepts again later, but those will have to be another day. It is exciting for me that I've made it far enough in my understanding of maths to start building anything this complex.
I've also just learned how to use the Animation Nodes "Reassign" loop output - which allows me to take the previously output value from a generator loop and use it as the starting value for an input of the same data type in the next execution of that loop, so things are about to get REALLY interesting in my production workflow. >:)
Hours after all of the original reference articles and videos that I read and watched,, hours after creating and becoming satisfied with my disign - when my final render was already in progress, I found Daniel Shiffman's "Lorenz Attractor in Processing" video, and thought to myself: "This guy is awesome. He gets straight to the point of what I wanted to learn. I wish I had come across this video first."
Edit: cross-linking to the Technical Variant
Lorenz Distractors: Technical Variant - Animation & 4K UHD+ wallpaper
http://imgur.com/gallery/KkskH
Animation Nodes v1.6 release announcement:
http://www.blendernation.com/2016/06/02/animation-nodes-1-6-improves-ux-adds-animation-baking
The beautiful render which initially inspired me was by Robert Trirop:
https://twitter.com/robert_trirop/status/716409341608329216
Daniel Shiffman's Coding Rainbow: The Lorenz Attractor in Processing
https://www.youtube.com/watch?v=f0lkz2gSsIk
A video of some super pretty 1984 vector display renditions of the Lorenz Attractor equation with multiple input parameter configurations:
https://www.youtube.com/watch?v=CeCePH_HL0g
More about the Maths:
https://en.wikipedia.org/wiki/Attractor#Strange_attractor
https://en.wikipedia.org/wiki/Phase_portrait
Bonus, because I couldn't -not- think this phrase while doing all the reading earlier: "Your MOM was a complex quadratic polynomial LAST NIGHT! OHHHHHH~!!"