Patent Document ID: 8484264
Application ID: 12877922
Patent Flag: 1

Claim One:
1. A machine-executed method comprising: determining, by a machine executing stored instructions, a topological categorization of an interval escape sequence constructed of inclusive intervals beginning with a coverage cell chosen as an initial iterate from a parameter space and iterating a metacomplex iteration expression, wherein determining the topological categorization comprises: determining, by the machine executing stored instructions, a cell state for cell iterate data as an incomplete state when an interval defined by a last iterate does not overlap an origin, and the interval defined by the last iterate does not exceed a category escape distance, determining, by the machine executing stored instructions, a different state that is one of: an indeterminate state when the interval defined by the last iterate overlaps the origin, or an escape category when the interval defined by the last iterate exceeds the category escape distance; calling, by the machine executing stored instructions, on interval operators from a pool of inclusive interval operators to determine a parametric interval iterator of interval iterate data through one level of iteration of the metacomplex iteration expression, updating, by the machine executing stored instructions, the cell iterate data using a level iterator method comprising: when said cell iterate data is empty, initializing, by the machine executing stored instructions, the empty cell iterate data to a set of intervals of at least one interval, wherein said set of intervals covers said coverage cell, and, when the cell iterate data is not empty, updating, by the machine executing stored instructions, said cell iterate data with interval results from applying said parametric interval iterator to each interval of the last iterate of said cell iterate data, determining, by the machine executing stored instructions, an interval escape iterator of said coverage cell beginning with the cell iterate data initialized to empty, and looping, by the machine executing stored instructions, through successive applications of said cell iterate data to said level iterator method until the different state is determined; determining, by the machine executing stored instructions, said topological categorization based at least in part on the different state and said cell iterate data.