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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
How did you get the smooth curves while the series itself increased discretely?
Great question. I'll add it to the thread.
aⁱˣ - Any number raised to a multiple of i produces a number between -1 and 1. Do you have a good explanation for why?
@3blue1brown has a great video on the intuition behind e^ix
Oh I made a tool to visualize exponential sums in the browser. Maybe you find it interesting?https://twitter.com/anvaka/status/1159836176238252034?s=19 …
Play with it here: https://anvaka.github.io/e-sum/?code=x%2F8%20%2B%205*cos%28x*101.824%29%20&bufferSize=12000&totalSteps=300000&spi=500 … pic.twitter.com/PQ8bGTLDazi will be back. e will make sure of it.
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