One of the best designed visualizations of a non-intuitive concept I've ever seen. One could show this video at the beginning of class and have 50 minutes worth of discussion / questions from class of vif undergrads. If I may ask: How many iterations & time till final product?
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thanks! i've been working on my animation skills for years, but i've been making dynamical systems vids for ~4 months at the rate of 2-3/week. this particular vid took several days to get right in my head, but about 1 day of programming & rendering. this was the first take.
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Wowowow this just made the connection for me that complex eigenvalues must always come in pairs because spirals happen in a *plane*!
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Yes, and this is why rotating a body in an odd dimensional space must leave one axis invariant... The number of complex eigenvalues must be even.
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This would be of tremendous value in an ODEs class, early on!
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indeed.
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Very intriguing. Although what do you mean by the 'flow' in here ?
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the solutions to the differential equations x'=Ax form a flow
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Re is the Reynolds’s number? Also, what language/apis are you using to program this? I use Blender/Animation Nodes for most of my visualizations.
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the axes are the real (Re) and imaginary (Im) parts of the eigenvalues. sorry i could not explain better, but... twitter [character limits]. blender is great! highly recommended.
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