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I have been working on this video for two weeks. Since I make these with coding, the simulation is itself really easy, but the Slow-motion, Zooming and shifting the camera at key moments is the hardest nightmarish part, Almost gave up multiple times , The original video was 110000 frames, but for this short I had to speed it up to fit in 60 seconds. But on my Instagram you can find 90 seconds of extended version with 300k frames. I programmed this on python, the graph is plotted and animated with “matplotlib“ library. The graph is visualized on complex plane, Here is the function : z(θ)=e^θi e^(⋅θi) θ = Angle made by the Inner Arm e = Euler's constant i = Imaginary number The first half of the equation e^θi represents the inner arm and second half of the equation represents the outer arm. This simulation animates the angle θ from 0 to approximately 52000 degrees. The visual illustrates a setup where the outer arm is rotating golden ratio times faster than the inner arm. Since the golden ratio is an irrational number with infinite digits, the line would never connect to its starting Position, no matter how long, how fast we run this simulation. If you zoom in you'd always see the gap between those lines. Hence it fills every possible space enclosed within a circle.
