Function Repository Resource:

# FoliationClass (1.0.0)current version: 2.0.0 »

Generate the foliation set from the causal graph coordinate data input

Contributed by: Tom Lee, Jon Lederman  |  Tom Lee
 ResourceFunction["FoliationClass"][data] returns the foliation set from the causal graph coordinate data.

## Details

The data input should be a set of the coordinates with a numbered index for the casual nodes.
For example, the data set {{1, 0, 1}, {2, 0, 3}, {3, 2, 4}} represents three-point coordinate information of the triangular shaped causal graph. The first element of each set is the index of the point, eg. point 1, point 2, point 3. The second and third elements are the temporal and spacial coordinates, e.g. point 1 is the event at time=0, space=1.
Foliation is the process of categorizing the point with the time coordinate. For example, the data set {{1, 0, 1}, {2, 0, 3}, {3, 2, 4}} the point 1 and 2 are on the same temporal line, and the point 3 is in a different foliation.
Causal graphs inputs can be generated using the resource function SimpleCausalGraphCoordinates.
The function returns the categorized point index where each element represents a node. For example, for the data set {{1, 0, 1}, {2, 0, 3}, {3,2,4}} the function returns {{1,2},3}.
By using different causal data set instead of using SimpleCausalGraphCoordinates function, one can generalize the causal graph structure with arbitrary rewriting rules.

## Examples

### Basic Examples

Find the foliation of three causal points in Euclidean coordinates:

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Construct the simple triangular shape (type 1) causal graph with initial node size 10:

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See the triangular shape:

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Apply the function to find the foliation:

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## Version History

• 2.0.0 – 15 June 2022
• 1.0.0 – 07 June 2022