N hard spheres in a box.

N=1: Velocity space is 3-dimensional, with a 2-dimensional spherical energy surface. To demonstrate the equal a priory density on the energy surface we project the spherical surface onto a rectangle, using Lambert's area preserving (and therefore density preserving) projection.
Interestingly, the velocity density p(v_x) is now a constant.

N>1: Velocity space has 3N dimensions. The statistical distributions evidently approach the large-N limits.
In particular, the velocity density p(v_x) already resembles a Gaussian.

[Code: Hspheres]