Uploaded April 2023 | Updated September 2026, 2 weeks ago
Suggested by several viewers in another videos. Thanks for commenting and suggesting stuff.
The function is indeed minus cos(x) thus having a minimum around origin, but this does of course not impact the conclusion, i.e., that this is a chaotic system. Based on the (visual) conclusion that the x^4 polynomial is chaotic (see youtube.com/watch?v=QyJYkqEsuRE), it's unsurprising that cos(x) is so too, since cos(x) = 1- x^2/2 + x^4/4! - x^6/6! + ...
Balls are initially mutually separated by one millionth of the plot width, and do not interact with each other in any way.
Song: Stella by Starlight, originally made by Victor Young - here reproduced by @gpcbass (and used in several others of our videos).
Visuals in Python & FFmpeg.
Suggested by several viewers in another videos. Thanks for commenting and suggesting stuff.
The function is indeed minus cos(x) thus having a minimum around origin, but this does of course not impact the conclusion, i.e., that this is a chaotic system. Based on the (visual) conclusion that the x^4 polynomial is chaotic (see youtube.com/watch?v=QyJYkqEsuRE), it's unsurprising that cos(x) is so too, since cos(x) = 1- x^2/2 + x^4/4! - x^6/6! + ...
Balls are initially mutually separated by one millionth of the plot width, and do not interact with each other in any way.
Song: Stella by Starlight, originally made by Victor Young - here reproduced by @gpcbass (and used in several others of our videos).
Visuals in Python & FFmpeg.
