Uploaded October 2025 | Updated September 2026, 2 weeks ago
Really tricky one from a graphics rendering perspective. I tried many different chaotic billiard domains before ending up with this, each with many initial conditions, as well as log- and linear scaled histogram plots. This for making justice of the huge number of balls, and get a grasp of the number 10^9, i.e., one billion. I think there is much room for improvement though.
The histogram plots are linear and constant and are manually balanced with respect to saturation and minimum cutoffs, etc. Calculations were performed by using PyTorch with average step time of 0.1 s, where each 30th frame was saved to disk to suppress the sensitive discrete time effects in chaotic systems.
I ended up with the perhaps most well-known chaotic billiard out there - the Bunimovich (or "Stadium") billiard. This one has some really nice caustics geometry when modelling many balls, which I learned from this excellent video some years ago: youtube.com/watch?v=1ffiMs0CZzU
Cool music made by @gpcbass. The song is called Swing Zero and used a couple of times on this channel previously.
Really tricky one from a graphics rendering perspective. I tried many different chaotic billiard domains before ending up with this, each with many initial conditions, as well as log- and linear scaled histogram plots. This for making justice of the huge number of balls, and get a grasp of the number 10^9, i.e., one billion. I think there is much room for improvement though.
The histogram plots are linear and constant and are manually balanced with respect to saturation and minimum cutoffs, etc. Calculations were performed by using PyTorch with average step time of 0.1 s, where each 30th frame was saved to disk to suppress the sensitive discrete time effects in chaotic systems.
I ended up with the perhaps most well-known chaotic billiard out there - the Bunimovich (or "Stadium") billiard. This one has some really nice caustics geometry when modelling many balls, which I learned from this excellent video some years ago: youtube.com/watch?v=1ffiMs0CZzU
Cool music made by @gpcbass. The song is called Swing Zero and used a couple of times on this channel previously.
