Uploaded February 2019 | Updated September 2026, 2 weeks ago
This is the evil twin to my previous Circle Map render:
youtube.com/watch?v=-l12chlb31M
x ← x + Ω - K * sin(2πx) / 2π mod 1
This is another graph of the circle map iteration, but what was changing over time in the other rendering is now changing across the vertical, and vice versa.
mathworld.wolfram.com/CircleMap.html
Ω varies from 0 to 1 across a vertical row, and each row represents a single value of K from 4π to 0, left to right. Over time what varies is the initial value used for x.
Instead of keeping a trace of where the iterated values of x land across the vertical column, as the last render did, instead I am counting how many iterations it takes to return to the initial value (within some epsilon). If it never returns, the image is black. If it returns very quickly, the image is brighter.
This took a lot more processing time, and the result is very noisy Maybe a bit spooky. It would probably take an insane amount of time to reduce that noise, however. This is just a hazy approximate view into this strange chaotic system.
More info and example program:
patreon.com/posts/24826459
This is the evil twin to my previous Circle Map render:
youtube.com/watch?v=-l12chlb31M
x ← x + Ω - K * sin(2πx) / 2π mod 1
This is another graph of the circle map iteration, but what was changing over time in the other rendering is now changing across the vertical, and vice versa.
mathworld.wolfram.com/CircleMap.html
Ω varies from 0 to 1 across a vertical row, and each row represents a single value of K from 4π to 0, left to right. Over time what varies is the initial value used for x.
Instead of keeping a trace of where the iterated values of x land across the vertical column, as the last render did, instead I am counting how many iterations it takes to return to the initial value (within some epsilon). If it never returns, the image is black. If it returns very quickly, the image is brighter.
This took a lot more processing time, and the result is very noisy Maybe a bit spooky. It would probably take an insane amount of time to reduce that noise, however. This is just a hazy approximate view into this strange chaotic system.
More info and example program:
patreon.com/posts/24826459
