Practical empirical mathematics

Difference tables and polynomials

Implementation [of repetitive array]

Implementation [of finite automata for nested patterns]

[Patterns from] arbitrary digit operations

Generating functions [for nested patterns]

Standard mathematical functions

[Generating functions for] 1D sequences

Multidimensional additive rules

Continuous generalizations [of additive rules]

[Algebraic computation of] additive cellular automata

The more general case [of computation speed ups]

Cellular automaton [Boolean] formulas

Cellular automaton [Nand] formulas