Another class-inspired animation; meet the homoclinic tangle!
A rainbow of closely packed points hop on the plane according to a simple rule. As they hop, they spread out, and their hopping patterns get more & more different to their neighbors'—a classic symptom of chaos. #mathpic.twitter.com/1NuGBEkCNx
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Eventually, they'll all fly out to infinity, but at differing times; and how/when that occurs is very sensitive to their starting points. That's called transient chaos! It's all thanks to the "rule" causing those goofy patterns near (1,0)—that's (part of) the eponymous tangle.
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The homoclinic tangle itself is made up of all the points that eventually approach (1,0) as they hop, and the ones that eventually approach (1,0) if they had started hopping in reverse.
#mathematics Here's what it (approximately) looks like. Weird, isn't it?pic.twitter.com/kAIcRNgkER
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You can get a sense of what nonlinearity does to the hopping "rules" by looking at where a dense group of points go after about ~15 hops forward/backward for varying k. (This is technically HW for
@stevenstrogatz's dynamical systems course—it's tough to hand in a GIF in person!)pic.twitter.com/ifAv64c87z1 reply 12 proslijeđenih tweetova 63 korisnika označavaju da im se sviđaPrikaži ovu nit -
Odgovor korisnicima @Arnaldo_AGITF @stevenstrogatz
You so rock
@Arnaldo_AGITF ! I’m having fun watching your fun with chaotic homework.1 reply 0 proslijeđenih tweetova 3 korisnika označavaju da im se sviđa
Thank you @amyhodler! If you're interested in nonlinear dynamics/chaos animations in general, I made a bunch more of 'em while taking an intro to chaos class last year; they're on YouTube (https://tinyurl.com/y4qsh9dg ) and buried down my Twitter feed. Hope you like them!
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