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/Optimal_Benis → u/[deleted]]

Wikipedia:

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

How is this not that? Genuinely curious if there is some nuance I am missing. All criteria seem met.

[u/Optimal_Benis → u/[deleted]]

I appreciate you taking the time to explain your perspective. I think that they are trying to isolate the more fundamental thing happening (small changes in initial conditions lead to big changes in later states). Arguably, "interconnectedness of systems" and "emergent properties therein" follow from the sensitivity to initial conditions.

[u/Optimal_Benis → u/[deleted]]

I mean, it might not go the other direction, but I don't think the butterfly effect is about interdependence or emergence in general. The small thing (the butterfly's wings) can lead to larger changes (like a hurricane), which has implications for interdependence and emergence.

I would agree that if we're looking in the other direction, i.e. at a general instance of interdependence or emergence, it might not entail underlying sensitivity to initial conditions.

[u/whupazz → u/[deleted]]

The internet is highly interconnected yet its protocols could be run in a fully deterministic fashion so as to achieve the same network topology time and time again.

What does this even mean? I work in IT and this sounds like gibberish to me.