Spatial point process vs. spatial point pattern

• Spatial point process: a stochastic process $\{X_1, X_2, ..., X_{N(A)}\}$ taking values in a planar region $A \subset \mathbb{R}^2$.

  !! $N(A)$ is a random variable !!

• Spatial point pattern: a single realization of a spatial point process.

  Each realization has a different number of points and different locations.

  The points are also often referred to as events.