Illustration of how I would conceptualize an array-backed octree data structure, complete with ASCII art.

Octree Illustration

/*

  0 = 000: x-, y-, z-
  1 = 001: x-, y-, z+
  2 = 010: x-, y+, z-
  3 = 011: x-, y+, z+
  4 = 100: x+, y-, z-
  5 = 101: x+, y-, z+
  6 = 110: x+, y+, z-
  7 = 111: x+, y+, z+
  
  ASCII ART ~~~~~~~~~~~~~

       FRONT    
     +---+---+  Y
    / 3 / 7 /|  |
   /---/---/ |  +--X
  +---+---+| |
  | 2 | 6 ||.+
  +---+---+'5|
  | 0 | 4 ||.+ <--Positive Z
  +---+---+' <--Negative Z
  ^--Behind: 1
  
*/