System Types (5) 

MultiwaySystem supports both string and list substitution systems:

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Lists can contain arbitrary symbolic elements:

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Give an explicit substitution system rule:

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An alternative method of specifying that a substitution system should be used:

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MultiwaySystem also supports multiway generalizations of cellular automata:

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Lists of cellular automaton rules can also be specified directly:

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Generate a states graph from left- and right-shift cellular automaton rules:

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Generate a causal graph for the rule 30 cellular automaton:

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MultiwaySystem also supports multiway generalizations of Wolfram models:

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Generate an evolution causal graph for a Wolfram model rule:

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Construct a multiway system by explicitly specifying an association:

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Rules and Initial Conditions (2) 

MultiwaySystem accepts both individual rules and lists of rules:

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Likewise for initial conditions:

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Event Selection Functions (4) 

Apply only the first possible event at each step:

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Apply the first and last possible events at each step:

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Use a greedy-style algorithm to apply the maximal set of nonconflicting events at each step (strings only):

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Compare this to the full states graph:

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State Node Rendering (5) 

By default, states are labeled by their contents:

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Use no labeling for states:

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"StatesGraphStructure" yields the same result:

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Use raw state names as node labels:

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Use a named shape as each state label:

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Event Node Rendering (5) 

By default, both states and events are labeled by their contents:

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Use no labeling for states:

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Also use no labeling for events:

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"EvolutionEventsGraphStructure" yields an equivalent result:

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Use raw event expressions as their labels:

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Initialization Events (3) 

By default, "AllEventsList" does not include initialization events:

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The option "IncludeInitializationEvents" allows one to override this default:

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Initialization events have special default rendering:

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Graph Layout Options (2) 

Place arrows in the middle of edges:

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Generate an example multiway evolution from page 209 of A New Kind of Science:

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Force the initial state node to be at the top:

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Step Numbers and State IDs (4) 

By default, equivalent states are merged across all time steps:

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Merging of equivalent states across different time steps can be prevented by including step numbers:

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Merging of equivalent states at the same time step can be prevented by also including state IDs:

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Step numbers and IDs also apply to events:

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Event Instances (2) 

By default, multiple instances of equivalent updating events are merged in the states graph:

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Merging of equivalent events can be prevented by including event instances:

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State (Path) Weights (2) 

Vertices of a states graph can be weighted by their relative rate of occurrence at each time step:

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Vertices can also be weighted by the number of distinct evolution paths that lead to them:

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MaxItems (2) 

By default, "CausalGraphInstances" returns all possible causal graphs:

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The number of causal graphs returned can be limited using MaxItems:

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Predecessors and Resolvents (2) 

By default, "BranchPairsList" returns only a list of branch pairs:

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Common predecessor states can be shown using "GivePredecessors":

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Similarly, "BranchPairResolutionsList" by default lists only resolved and unresolved branch pairs:

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Common resolvents of resolved branch pairs can be shown using "GiveResolvents":

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Show both common predecessors and common resolvents, where appropriate:

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Self-Pairs (2) 

By default, "CanonicalBranchPairsList" does not include self-pairs (i.e. trivial critical pairs):

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Self-pairs can be included using "IncludeSelfPairs":

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Full Branchial Space (2) 

By default, non-branch pair states are not shown as part of the branchial graph:

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They can be shown using "IncludeFullBranchialSpace":

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Causal Invariant Rules (3) 

Show the state graph structure for a multiway system:

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Show the causal graph structure:

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Show that this multiway evolution is both causal invariant and total causal invariant:

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Illustrate a simple sorting rule:

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Generate string replacements rules corresponding to the Xor function:

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The multiway system has many paths, but due to causal invariance all lead to the same eventual result:

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The And function is also confluent, since it too is associative:

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The Nand function is not associative, so can lead to different results:

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