Function Repository Resource:

# MultiwayEvolutionPlot

Plot the evolution of a multiway system

Contributed by: Stephen Wolfram and Jonathan Gorard
 ResourceFunction["MultiwayEvolutionPlot"][rules,init,n] plots the first n steps in the evolution of the multiway system with the specified rules starting from initial conditions init.

## Details and Options

ResourceFunction["MultiwayEvolutionPlot"] currently only works for string substitution rules of the form {"lhs"1"rhs"2,}.
Options for ResourceFunction["MultiwayEvolutionPlot"] include:
 "EvolutionEventRendering" "SingleArrow" how to render the events in the evolution "VerticalSpacing" 2 vertical spacing between rows "HorizontalSpacing" 1.5 horizontal spacing between elements
Possible settings for "EvolutionEventRendering" include:
 "SingleArrow" a single arrow between connected states (as in A New Kind of Science) "PositionalArrows" arrows indicating the center of each rewrite event "PositionalPolygons" polygons indicating the extent of each rewrite event
ResourceFunction["MultiwayEvolutionPlot"] accepts both individual rules and lists of rules, and likewise for initial conditions.

## Examples

### Basic Examples (3)

Plot a basic multiway evolution:

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Plot a more complicated multiway evolution with arrows showing the rewrite events:

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Plot the same multiway evolution but with polygons highlighting the rewrite events:

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### Scope (2)

MultiwayEvolutionPlot accepts both individual rules and lists of rules:

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Likewise for initial conditions:

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### Options (2)

Default plot with single arrows between states:

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Separate arrows indicating the center of the beginning and end of each rewrite event:

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Polygons indicating the extent of the beginning and end of each rewrite event:

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Specify spacings in terms of element sizes:

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## Version History

• 3.0.0 – 10 April 2020
• 2.0.0 – 19 March 2020
• 1.0.0 – 10 March 2020