Concerning Fox 217 from http://www.8foxes.com
A random process on the plane is defined as follows:
It starts from point 0. Then the following point is generated in a
randomly-selected direction, 1 unit apart from the previous one.
The process stops the first time 1 (or more) closed area(s) is obtained.
What is the average number of steps taken?
Specifically, what is the probability that a closed area will be created in three steps?