A 2D Poisson point process with intensity λ generates random but statistically uniform points. Explore Voronoi tessellations, nearest-neighbor distances, and inhomogeneous intensities.
Homogeneous Poisson: N ~ Poisson(λ·Area), points uniform. Nearest-neighbor dist: F(r) = 1 − exp(−λπr²) (Rayleigh). Voronoi cells have mean area 1/λ, area distribution ~ Gamma. Inhomogeneous: λ(x,y) varies — intensity shown as background glow.