Chaos.

Step 1 of 4

The same start

A double pendulum is a rod hanging from a pivot, with a second rod hanging from its end. The scene has two, a blue one in front and a pink one behind it, built exactly alike and released together from $120^\circ$⁠. Their motion is computed from Newton’s laws, with no dice anywhere.

Step 2 of 4

A tiny gap

Now the pink one starts $0.01^\circ$⁠ further round, a difference you cannot see. Show the paths shows each pendulum’s path, and a chart of the gap between them on a log scale: each square up is ten times more. On the board a timer shows the time since release and the gap now.

Step 3 of 4

Ten times the precision

On the chart the gap climbs in an almost straight line. On a log scale a straight line means exponential growth: in each fixed stretch of time the gap is multiplied by the same number. A system in which tiny differences grow like this is called chaotic, and this dependence on the start is called the butterfly effect.

Step 4 of 4

A gentle release

Not every motion of a double pendulum is chaotic. The Release angle is free now.

Try it: after checking, find roughly the angle at which the motion turns from regular to chaotic. The chart will tell you.

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