Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Produce causal graphs by dynamically triangulating a specified region of a (potentially curved) spacetime
ResourceFunction["CurvedSpacetimeTriangulation"][cond,{x_{1},…,x_{n}},meas] produces a dynamical triangulation of a (potentially curved) spacetime region that satisfies the conditions cond.  
ResourceFunction["CurvedSpacetimeTriangulation"][cond,{x_{1},…,x_{n}},{{x_{min},x_{max}},…},meas] restricts the triangulation to the bounds {x_{min},x_{max}}×….  
ResourceFunction["CurvedSpacetimeTriangulation"][cond,{x_{1},…,x_{n}},meas,"prop"] gives the property "prop" for the specified triangulation.  
ResourceFunction["CurvedSpacetimeTriangulation"][cond,{x_{1},…,x_{n}},{{x_{min},x_{max}},…},meas,"prop"] gives the property "prop" for the specified restricted triangulation. 
"CausalGraphFull"  full causal partialorder graph (before transitive reduction) 
"CausalGraph"  transitively reduced causal partialorder graph 
"TriangulatedCausalGraphFull"  full causal partialorder graph using only triangulation edges (before transitive reduction) 
"TriangulatedCausalGraph"  transitively reduced triangulated causal partialorder graph 
"Points"  plots of the points in the triangulation (without causal edges) 
"PointsList"  list of spacetime coordinates of all points in the triangulation 
"PointsCount"  number of points in the triangulation 
"Dimensions"  number of dimensions in the continuum spacetime approximation 
"TriangulatedEdgeList"  list of (undirected) edges that appear in the triangulation of the spacetime surface 
"TriangulatedEdgeCount"  number of (undirected) edges that appear in the triangulation of the spacetime surface 
"MaximumCellMeasure"  maximum measure (e.g. area, volume, etc.) meas of the simplices appearing in the triangulation 
"TotalEdgeCount"  total number of causal edges (before transitive reduction) 
"ReducedEdgeCount"  number of transitively reduced causal edges 
"TotalTriangulatedEdgeCount"  total number of causal edges that are also triangulation edges (before transitive reduction) 
"ReducedTriangulatedEdgeCount"  number of transitively reduced causal edges that are also triangulation edges 
"PureCausalGraphFull"  full causal partialorder graph (before transitive reduction) with vertex coordinate information removed 
"PureCausalGraph"  transitively reduced causal partialorder graph with vertex coordinate information removed 
"PureTriangulatedCausalGraphFull"  full causal partialorder graph using only triangulation edges (before transitive reduction) with vertex coordinate information removed 
"PureTriangulatedCausalGraph"  transitively reduced triangulated causal partialorder graph with vertex coordinate information removed 
"MeshRegion"  mesh region corresponding to the triangulated spacetime surface 
"MeshConnectivityGraph"  connectivity graph of the mesh region corresponding to the triangulated spacetime surface 
"Properties"  list of properties 
Produce a triangulation of a 1+1dimensional hyperbolic region of spacetime into simplices of measure (area) up to 0.1:
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Show the causal graph:
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Show the full causal graph (without transitive reduction):
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Show the causal graph using only triangulation edges:
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Show the mesh region corresponding to the triangulated spacetime surface:
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Show the connectivity graph of this mesh region:
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Produce a triangulation of a 2+1dimensional hyperboloidal region of spacetime (i.e. de Sitter space) into simplices of measure (volume) up to 1:
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Show the causal graph:
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Show the pure causal graph (with vertex coordinate information removed):
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Show the pure causal graph with a layered graph embedding:
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Show only the pure triangulated causal graph (with vertex coordinate information removed):
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Produce a triangulation of a 2+1dimensional paraboloidal region of spacetime based on Flamm's paraboloid (related to the Schwarzschild geometry) into simplices of measure (volume) up to 0.1:
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Plot the positions of the points in the triangulation only (without causal edges):
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Show the causal graph:
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By default, the region is restricted to the bounds {{1,1},…}:
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Show the causal graph:
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Triangulations can be produced for 0+1dimensional spacetimes:
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Show the pure causal graph:
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Produce a triangulation of a 1+1dimensional spacetime:
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Show the causal graph:
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Produce a triangulation of a 2+1dimensional spacetime:
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Show the pure causal graph:
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Properties can be requested directly from CurvedSpacetimeTriangulation:
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Produce a triangulation of a 1+1dimensional hyperbolic region of spacetime into simplices of measure (area) up to 0.1:
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Show the complete list of properties:
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Show the full causal graph:
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Show the transitivelyreduced causal graph:
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Show the full causal graph using only triangulation edges:
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Show the transitivelyreduced causal graph using only triangulation edges:
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Plot the positions of the points in the triangulation only (without causal edges):
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Show a complete list of spacetime coordinates for the points in the triangulation (the last coordinate is always the time coordinate):
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Show the number of points in the triangulation:
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Show the number of dimensions in the background spacetime:
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Show the first 50 (undirected) edges in the triangulation of the spacetime surface:
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Show the total number of (undirected) edges in the triangulation of the spacetime surface:
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Show the maximum measure (in this case, area) of the simplices in the triangulation:
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Show the total number of causal edges:
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Show the number of causal edges after transitive reduction:
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Show the total number of causal edges appearing in the triangulation:
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Show the number of causal edges appearing in the triangulation after transitive reduction:
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Show the pure full causal graph (with vertex coordinate information removed):
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Show the pure transitivelyreduced causal graph (with vertex coordinate information removed):
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Show the pure full causal graph using only triangulation edges (with vertex coordinate information removed):
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Show the pure transitivelyreduced causal graph using only triangulation edges (with vertex coordinate information removed):
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Show the mesh region corresponding to the triangulated spacetime surface:
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Show the connectivity graph of this mesh region:
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