What are the properties when you increase a double pendulum to infinite numbers of pendulums?

It would look very herky jerky. The movement of a double pendulum is chaotic and sensitive to initial conditions. Anything more than double would be even more chaotic. Wikipedia article

@LostInParadise I wonder if in the chaos you will get order? Maybe if we start with a triple pendulum and increase one at a time?

Maybe if you had a lot of them, the ones on the top would be carrying so much weight that they would not move much, but the ones on the bottom would be jerking around all over the place.