Quoting the author: “Whenever I animate more than one ball in these animations, the starting positions are slightly different. For chaotic systems, like this, the distances between the balls increases exponentially.”

Video description: "In the 1000-ball part balls are initially mutually separated by less than a millionth of the plot width. "

I was wondering this too! The video description states:

> In the 1000-ball part balls are initially mutually separated by less than a millionth of the plot width.

Right. Also I think the initial drop position is deliberately selected to get the balls separating sooner. Once they get over the hump to the right side, they make several successive bounces at very shallow angles to the surface, which will magnify a small difference in ball position into a greater difference in bounce position and timing.

They don't have the same initial condition. It appears that in the rendering because it has a much lower resolution than the simulation it is rendering.