Why are icicle long and thin?

Here is a great image of three icicles.

As water drips onto an icicle and freezes, it releases heat. The warm air rises up the sides of the icicle. That warm air layer acts like a blanket that’s an insulator, and so the blanket is very thin near the tip and thick at the top. That allows the top to grow very slowly and the tip to grow rapidly — creating a long, thin icicle.

The height of an icicle is proportional to the radius to the four third!

The apex angle is about 15 degrees

How the ripples form on the icicle issue has not been fully resolved yet. I am not even sure if the problem of optimal distance between the icicles has been resolved either!