eⁱˣ = cos(x) + i sin(x)pic.twitter.com/4fCuF4LOY3
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A natural question is: Why is this animation smooth? The answer is that you can define the so-called fractional derivative, which generalizes nth derivative to a real number of derivatives The fractional Taylor series smoothly interpolates between integer derivativespic.twitter.com/757q5yvu7k
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is this animation made via manim ?
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no, mathematica
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Very nice. I also think it looks nice read as x = (1/4)τ, (2/4)τ, (3/4)τ, (4/4)τ
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Damn this is the gif that keeps on giving
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What is this?
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is there a pattern in when each of the points stabilize? it looks like the points "stabilize" at t = 4, 8, 12, 16. I wonder if the points e^(i n pi/2) "stabilize" at t = 4n, or something like that. I'm using stabilize as "stays within a ball of small radius"
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There are theorems bounding the error for Taylor estimates in real variables, but I don't know any for complex ones
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This is an excellent visual well done!!!
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this is so beautiful
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