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About Alexander Gustafsson
Physics and mathematics simulations accompanied by music made by @gpcbass (link below).
Located in Växjö, Sweden.
Recent Videos from Alexander Gustafsson
Hourglass billiard
Ball/ray moving and elastically bouncing in a domain reminiscent of an hourglass. Pretty useless for being an hourglass though.
Song made by @gpcbass, used previously on this channel.
Visuals in Python & FFmpeg. Egg billiard
Balls elastically bouncing in a two dimensional egg-shaped mathematical billiard are shown. The egg contour is defined by x^2 + (1.4^x * 1.6y)^2 = 1 (equation discovered by Don M. Jacobs).
1. One ball bouncing inside the egg contour.
2. 10 000 normally distributed balls moving in the same.
3. Sa… Butterfly effect in an elliptic curve but not in an ellipse
Billiard comparison between the bounded region of the function y^2 = x^3 - x (elliptic curve; see https://www.wolframalpha.com/input?i=y%5E2+%3D+x%5E3-x) and x^2 + ay^2 = 1 (ellipse). For certain initial conditions, the elliptical curve system exhibits a chaotic behaviour, i.e., "butterfly effect" …
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