Random Polygons

Polygon illuminated by central lamp Polygon generated from random permutation of n points
Two random polygons generated with different algorithms:

Background of the problem

A fractal approach -- start with n-1 gon; construct n-gon.

Finding the nth point randomly and fairly

Step 1
Step 2
Step 3
Step 4
Step 5
Step n
Being careful

Showing that it always works

Time considerations