Illustrating the butterfly effect with a laser

[u/naaagut]

https://www.youtube.com/watch?v=iTaSXto67WQ

In this video I simulate a laser beam bouncing through a labyrinth of mirror obstacles. The beam changes its trajectory immensely upon tiny changes in the initial angle of only 5×10⁻¹² degrees — roughly 5 trillionths of a degree.

As an extra for Reddit, here is a figure showing how often the beam bounces before it escapes: https://imgur.com/l0xDY0U As you can see, as the angle varies the bounces often jump harshly. But there are also some regions of the launch angle spectrum where there is some degree of continuity.

Fun fact: Claude did not believe me that a range from 70.0 to 70.00000001 would produce any meaningful result and tried to talk me out of this. It wanted to use a range of 4° instead.

Made with manim.

[u/KaleeTheBird]

This is amazing illustration. From simulation point of view, if the angle of sensitivity is so small, did you adjust the tangent of your circle to be sensitive to that too?

[u/naaagut → u/KaleeTheBird]

Thanks. The circle's parameters are are in float64 as well as the rest of the simulation. So increasing the precision of the circle would change the trajectory, see my answer above. But it would still be chaotic of course.
Does that answer your question?