Table 3
Derivatives 1 through 4 for four basins

Visual comparisons of patterns in various TAO columns makes evident how categories of basins are generated.

   
NOTE: The categories used to sort basins in Table 2 above and throughout this running example are based on rotating all derivatives so that they begin arbitrarily with the iteration that has the lowest Boolean value (starting the Boolean expression from the first node, top, down to the last node bottom). In the visual representation above white equals 0 and black equals 1. For example, scan down the first column of Basin 60's TAO-1 column and notice that when you get to the little checker board area TAO would rotate first derivative so that first row of the checker board starts with a white square, i.e., a Boolean 0. That would start basin 60's derivative with its lowest possible Boolean value and would adjust its phase with the TAO-1 pattern for basin 76.