Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://reference.wolfram.com/language/ref/SubstitutionSystem.html below:

SubstitutionSystem—Wolfram Language Documentation

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technology expertise.

• Data & Computational Intelligence
• Model-Based Design
• Algorithm Development
• Wolfram|Alpha for Business
• Blockchain Technology
• Education Technology
• Quantum Computation

WolframConsulting.com

• See Also
  • RulePlot
  • NestList
  • Replace
  • SequenceReplace
  • StringReplace
  • Flatten
  • ArrayFlatten
  • ThueMorse
  • RudinShapiro
  • CellularAutomaton
  • AnglePath
• Related Guides
  • Iterated Maps & Fractals
  • Computational Systems
  • Discrete Mathematics
  • Boolean Computation

SubstitutionSystem[rule,init,t]

generates a list representing the evolution of the substitution system with the specified rule from initial condition init for t steps.

• In SubstitutionSystem[rule,…], rule can be of the following forms:
• {i₁rhs₁,i₂rhs₂,…} list substitution system {"s₁"rhs₁,"s₂"rhs₂,…} string substitution system
• In list substitution systems, the rhs_i can be lists of any length or can be rectangular arrays of any depth but all with the same dimensions. They can also be individual elements such as integers.
• In string substitution systems, the rhs_i can be strings of any length.
• Both lists and string substitution systems can have rules that involve patterns, but every object that appears in the rhs_i must have a transformation defined by the rules given.
• List substitution systems work with SparseArray objects.
• In string substitution systems, the initial condition init must be a string; in list substitution systems, it must be an array whose depth is equal to the depth of the rhs_i.
• In SubstitutionSystem[rule,init,tspec], the time specification tspec can have any of the following forms:
• t all steps 0 through t {t} a list containing only step t {t₁,t₂} steps t₁ through t₂ {t₁,t₂,dt} steps t₁, t₁+dt, …
• SubstitutionSystem uses the first substitutions that apply at each step, in the same way as SequenceReplace and StringReplace.

Five steps of a string substitution system:

Analogous substitution system with lists:

Steps in a 2D substitution system:

Give the fourth step only:

Alternative form:

Generate a rule icon for a substitution system:

Lists do not have to be the same length:

The initial condition can be of any length:

Rules can involve patterns:

Arrays do not have to be square:

Arrays can have any depth:

The right-hand side of a rule can be a SparseArray:

SparseArray as an initial condition:

A string substitution system:

Use any characters in the strings:

Arrange output in a column:

Characters that do not appear in the rules are not replaced at each step:

Include additional characters in rules:

Steps 0 through 5:

Step 5 only:

Steps 3 through 5:

Odd-numbered steps:

Apply a single step of evolution:

Apply in operator form:

Set up neighbor-dependent string rules; rules are applied in the order given:

Steps in constructing a Cantor set:

Create an analogous 2D nested object:

3D Menger sponge:

Generate a "C curve" fractal:

Approximate a Cantor staircase function:

Generate steps in a Thue–Morse substitution system:

The output at each step k is given by ThueMorse[Range[0,2^k-1]:

3D substitution system based on the Levi–Civita tensor:

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4