MODULO PARTIAL MAPPING OF FRACTAL POTENTIAL AND FIELD LINES

摘要

Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.

主权项

1. A machine executed full modulo iterator method for creating a modulo point from a predetermined point iterate data, a predetermined point iterate goal, a predetermined winding digit adjustment, and a predetermined complex iteration expression, comprising:
(A) providing a branchcut adjuster means to return a winding count adjustment for a predetermined receiver point by counting directional transversal of the negative axis branchcut arising from the shortest rotation angular adjustment to rotate from a predetermined donor point to said predetermined receiver point, (B) providing a complex dominant splitter means for separating said predetermined complex iteration expression into a dominant expression as the term having the highest degree of an iteration variable and setting an inferior expression to the remainder of the expression, (C) providing a self winding operator pool means for returning a winding operator from a pool of the winding operators based on a predetermined winding operator request, (D) providing a self winding dominant stepper means for returning a winding point resulting from iterating said dominate expression in a predetermined iteration direction, using a predetermined point iterate data, by utilizing the winding operators from said self winding operator pool means, (E) providing a modulo banding creator means to construct a modulo point from a predetermined modulo banding parameters, (F) providing a full modulo resolver means to create a modulo point by calling said modulo banding creator means with said predetermined modulo banding parameters of (E) constructed by iterating said predetermined point iterate data to achieve said predetermined point iterate goal.