Sketch with 80 points

and a sketch with 10 points showing a kdTree with 3 dimensions and a median function as described in wikipedia

Numbers indicates the depth of the tree (also as a function of the size of plane),
red lines between points as leftChild, blue lines between points as rightChild

Drawn as tree diagram

kdTree: http://en.wikipedia.org/wiki/K-d_tree
Binary Space Parition: http://en.wikipedia.org/wiki/Binary_space_partitioning