Patent ID: 8402076

Claim:
A machine executed escape distance method to return an escape distance for a metacomplex escape topology based on a predetermined metacomplex iteration expression, having an iteration variable, throughout a metacomplex parameter space to determine an escape distance, comprising: (A) separating, by a dominant splitter on a machine, that separates said predetermined metacomplex iteration expression into a dominant expression as the term having the highest degree of said iteration variable, and setting an inferior expression to the remainder of said predetermined expression, (B) transforming, by a dominant reducer on the machine, said dominant expression into a real valued expression, called a real dominant expression, with absolute values taken of all factors so as to minimize the numerator and maximize the denominator, (C) transforming, by an inferior reducer on the machine, said inferior expression into a real valued expression, called a real inferior expression, with absolute values taken of all factors so as to maximize the numerator and minimize the denominator, (D) determining, by the machine, a predetermined real escape expression with substitution tokens called rde and rie, and with iteration token, called x, referencing the iteration variable, (E) determining, by an escape formula replacer on the machine, a substituted real escape expression constructed by replacing the rde token and the rie tokens with said real dominant expression and said real inferior expression, respectively, (F) determining, by a positive real root solver on the machine, the largest positive root by solving said substituted real escape expression equated to zero, for said x, wherein each of the steps from (A) to (F) are executed as parameters become available.