Mathematica: Computational Systems

CellularAutomaton -- general cellular automaton in 1D, 2D, etc.
TurningMachine -- general Tuning machine in 1D, 2D, etc.

SubstitutionSystem — general string, array, etc. substitution system in 1D, 2D, etc.

ShiftRegisterSequence — sequence from a linear or nonlinear feedback shift register

ThueMorse

RudinShapiro

expr/ .rule -- apply a rule
NestList -- interactively apply a function or evolution rule
NestWhileList -- iterate while checking for looping or termination
StringReplace, StringReplaceList -- rewrite, substitution, and multiway systems
ArrayFlatten -- flatten out steps in 2D substitution systems, etc.

Groupings- generate all possible trees applying binary, etc. operators to a list

RulePlot — visualize rules and evolutions of computational systems

ArrayPlot, ListPlot -- visualize arrays of data
GraphPlot, TreePlot -- visualize networks

FindSequenceFunction -- find functional forms for integer sequences

AnglePath — generate paths from angles

Boolean Functions:

    BooleanFunction
    BooleanTable
    BooleanConvert....

Referenced from: reference.wolfram.com