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Notes
Chapter 10
Section 11
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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