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22. Higher Fractal Roots

0. Context for Exploration

A. Number Family including rationals & irrationals
B. Patterns that transcend Beginnings
C. The primacy of the ‘seed’ in the Mandelbrot and Julia sets
D. History of what has been accomplished

1. Cube Root Algebra

A. The Fraction Series for the Cube Roots
B. Beginning Bogus Equations or Going Nowhere
C. Another method of iteration
D. A series of fractions or the F Series
E. The Denominator Series for Cube roots
F. The Three Basic Iterative Theorems for Cube Roots
G. Comparisons and parallels between cube and square root theorems

2. Fourth Root Algebra

A. The F Series for the 4th Root
B. The Denominator Series for the 4th Root
C. The Three Basic Iterative Theorems for Fourth Roots

3. General Root Algebra

A. The General Root Formula, F Series
B. The General Root Formula, D Series
C. Fractional Roots

4. Binomializing the F&D Series

A. The Binomialized F Series
B. Weird implications: inverted dimensions
C. Zero only exact number of our inverse universe
D. Binomializing the Denominator Series
E. Examples of D Series expansions
F. Three Basic Iterative Theorems for all Rational Roots

Summary & Conclusions