I think there is a link with curse of dimensionality here.
As you add more randoms, most of the points lie close to the surface.
This is also the case in high dimensional spheres: most of volume lie near the surface of the hyper sphere.
As you add more randoms, most of the points lie close to the surface.
This is also the case in high dimensional spheres: most of volume lie near the surface of the hyper sphere.
In the random() * random() * random() ... , once you draw at least one number close to 0 (chances will increase as you add more randoms), then your output collapses to a very small number. And in this visualization, 0 is shown as a point at the edge of the circle.
Of course with Euclidean it will as that seems to match our expectations for low dimensional space.
I'm not a mathematician so there is not much more that I could say on the matter at this juncture.
For p goes to infinity, the unit "ball" becomes a "cube" of two units wide per side.
https://en.wikipedia.org/wiki/Volume_of_an_n-ball#Balls_in_L...
https://www.johndcook.com/blog/2010/07/02/volumes-of-general...