Chapter 10: Processes of Perception and Analysis

Section 11: Traditional Mathematics and Mathematical Formulas

Practical empirical mathematics Difference tables and polynomials Implementation [of repetitive array] Nested patterns and numbers Implementation [of finite automata for nested patterns] [Patterns from] arbitrary digit operations Generating functions [for nested patterns] Pascal's triangle Nesting in bitwise functions Trinomial coefficients Gegenbauer functions Standard mathematical functions [Generating functions for] 1D sequences Multidimensional additive rules Continuous generalizations [of additive rules] Nested continuous functions GCD array Power cellular automata Computing powers [of numbers] Complex powers [of numbers] [Algebraic computation of] additive cellular automata The more general case [of computation speed ups] Evaluation chains Boolean formulas DNF minimization [Boolean] formula sizes Cellular automaton [Boolean] formulas Primitive [Boolean] functions Multilevel [Boolean] formulas Nand expressions Cellular automaton [Nand] formulas Binary decision diagrams History [of Boolean functions] Reversible logic [Reduced formulas in] continuous systems

From Stephen Wolfram: A New Kind of Science [citation]