Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Produce random spatial graphs by sprinkling points into a flat (Euclidean) Riemannian manifold
ResourceFunction["FlatManifoldToGraph"][dim,n] produces a random sprinkling of n points into a flat (Euclidean) Riemannian manifold of dimension dim, assuming a discreteness scale of 1. | |
ResourceFunction["FlatManifoldToGraph"][dim,disc,n] produces a random sprinkling of n points with discreteness scale disc into a flat (Euclidean) Riemannian manifold of dimension dim. | |
ResourceFunction["FlatManifoldToGraph"][…,"prop"] gives the property "prop" for the specified flat (Euclidean) Riemannian manifold sprinkling. |
"SpatialGraph" | spatial graph with vertex coordinates given by the underlying manifold coordinates |
"Points" | plot of the sprinkled points only (without spatial edges) |
"PointsList" | list of the manifold coordinates of all sprinkled points |
"DiscretenessScale" | discreteness scale of the sprinkling |
"PointsCount" | number of sprinkled points |
"Dimensions" | number of dimensions in the continuum manifold approximation |
"EdgeCount" | total number of spatial edges |
"PureSpatialGraph" | spatial graph with vertex coordinate information removed |
"Properties" | list of properties |
Produce a random sprinkling of 100 points into a 2-dimensional flat (Euclidean) manifold, with discreteness scale 0.3:
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Show the spatial graph:
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Show the pure spatial graph (with vertex coordinate information removed):
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Produce a random sprinkling of 200 points into a 3-dimensional flat (Euclidean) manifold, with discreteness scale 0.3:
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Show the spatial graph:
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Show the pure spatial graph (with vertex coordinate information removed):
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Plot the positions of the sprinkled points only (without spatial edges):
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By default, the discreteness scale is assumed to be equal to 1:
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Show the spatial graph:
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Sprinklings can be performed in arbitrary (integer) numbers of dimensions:
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In seven dimensions:
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Properties can be requested directly from FlatManifoldToGraph:
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Produce a random sprinkling of 200 points into a 2-dimensional flat (Euclidean) manifold, with discreteness scale 0.2:
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Show the complete list of properties:
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Show the spatial graph:
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Plot the positions of the sprinkled points only (without spatial edges):
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Show a complete list of manifold coordinates for the sprinkled points:
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Show the discreteness scale:
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Show the number of dimensions in the background manifold:
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Show the total number of spatial edges:
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Show the pure spatial graph (with vertex coordinate information removed):
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