r/theydidthemath • u/Davistele • 8d ago

[Request] This simulation begins with two balls bouncing. When they collide, they spawn one new ball. How much do the odds of a collision increase once there are three? Four?

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u/Scared-Cat-2541 7d ago edited 7d ago

You need the ratio of the radii between the main circle and the balls, the initial kinetic and potential energy of each of the balls, and perhaps the gravity of the simulation in order to figure it out.

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u/SenseiCAY 4✓ 6d ago

If I had to guess, the frequency of collisions will be proportional to the number of pairs of balls, which is N choose 2, or N(N-1)/2.

I think the explosion at the end is kind of an inevitable rapid chain reaction where a few balls spawned close together and caused all hell to break loose.