Exponential growth, but actually

It’s hyperbolic actually

Everything is balls

I liked how the other video did it better

Yeah the other video is more fun but not actually exponential

This is better i think. A new ball is added when two of them collide not everything they touch the boundary.

I love how in large enough numbers it appears there are groups moving in discrete directions. And when I swivel on my chair it appears there are swirls. My phone shows it at size of a silver dollar coin.

dn/dt ~ n^2, so n(t) ~ a/(1-bt) it's hyperbolic! reaches infinity in finite time

why assume the boundary matters

Challenge: make a simulation like this that has quadratic growth.

I think the version where it's when they collide with each other is more demonstrative. Unfortunately I haven't been able to find a version of that one without a bug at the end where the balls start spawning on top of each other and the circle is filled in a couple of frames.

Isn't this only approximately exponential at times before finite box size shows up in the statistics?

Yea except they have to start absorbing at a certain point to prevent the whole system from breaking fyi