Complete mapping of fractal potential and field lines

Abstract

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.

What is claimed is: 
     
         1 . A machine executed codomain point resolver method to convert a predetermined modulo point into a receiver codomain point by setting the field band integer of said predetermined modulo point based on a predetermined donor codomain point, comprising:
 (A) providing a codomain same level resolver means to set said field band integer based on disambiguating the enclosing decomposition region of said predetermined modulo point based on input of the field band fraction of said modulo point and the donor field band from said predetermined donor codomain point,   (B) optionally providing a codomain up level resolver means to set the receiver field band integer by calling said codomain same level resolver means on the field band fraction of said predetermined modulo point and the field band of said donor codomain point after adjusting the field band of said donor codomain point to appear to have a higher escape iteration count which matches the escape iteration count of said predetermined modulo point,   (C) optionally providing a codomain down level resolver means to set the receiver field band integer by calling said codomain same level resolver means on the field band fraction of said predetermined modulo point and the field band of said donor codomain point after adjusting the field band of said donor codomain point to appear to have a lower escape iteration count which matches the escape iteration count of said predetermined modulo point,   (D) providing a codomain resolve chooser means which chooses a means from those available in (A), (B), or (C) based on comparing escape iteration counts of said predetermined modulo point and said predetermined donor codomain point.   
     
     
         2 . The machine executed codomain point resolver method of  claim 1  wherein at least one of the optionally provided means of said codomain up level resolver means of (B) and said codomain down level resolver means of (C), is available for said codomain resolve chooser means of (D). 
     
     
         3 . The machine executed codomain point resolver method of  claim 1 , wherein both of the optionally provided means of said codomain up level resolver means of (B) and said codomain down level resolver means of (C), are present and useable by said codomain resolve chooser means of (D). 
     
     
         4 . A programmed machine comprising:
 one or more processors;   machine storage that stores instructions for performing the method of  claim 1 .   
     
     
         5 . A programmed machine comprising:
 one or more processors;   machine storage that stores instructions for performing the method of  claim 2 .   
     
     
         6 . A programmed machine comprising:
 one or more processors;   machine storage that stores instructions for performing the method of  claim 3 .