* Quad trees

  A few random thoughts on implementing [[https://en.wikipedia.org/wiki/Quadtree][quadtrees]]:  For clarity let’s describe them as representing
  pictures where each node represents a “pixel” whose size halves at each successive depth.  The
  content of a pixel can be thought to be a color.  We can pick a color (say 0) to represent pixels
  which are subdivided, i.e. represent inner nodes of the quad tree.  If we list the colors in BFS
  preorder then all the children of a given parent node are listed consecutively.  Being a quad tree
  it comes in clusters of 4.  Put this together with the coloring of parent nodes and a convention
  for the order of the children (say NW,NE,SW,SE) then all that’s required to understand the full
  structure is the color vector alone.  Since the root pixel is always subdivided (assuming a
  connected tree and not a forest) it’s always color zero and always first.  We don’t really need
  it.  What’s left is clusters of children.  We can just make this an Nx4 matrix.  Converting this
  to a classic parent vector is trivial.  Raze, find the zeros and repeat them four at a time.  To
  get the root back, bump up the indices by 1 and prepend a 0.