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Wolfram High School Summer Camp
3
Macy Maurer Levin
[WSC20] Visualisations of a Multiway Graph
Macy Maurer Levin, Stanford OHS
Posted
10 months ago
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A hypergraph is a graph in which edges, known as hyperedges, can join to multiple vertices, as denoted by the notation H = (V,
ϵ
), where V are the vertices made up of elements,
ϵ
.. In the Wolfram Model, hypergraphs depict space, and it is through these fascinating objects that it is hoped a proper model of the universe can be found. The objective of my project was to visualise one of these hypergraphs in such a way that the final result would resemble a Mollweide projection similar to that of the cosmic microwave background (CMB).
The Initial Visualisations
The first step of developing the visualisation was to choose a hypergraph from the Registry of Notable Universes off of the Wolfram Physics Project website. The hypergraph chosen for this project was W.M.1158, as pictured here.
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Then, taking the points collected from GraphEmbedding as well as the center of mass, a simple 3D graphic was constructed, allowing one to meddle with the x, y, and z axis of the graph and see what the hypergraph would look like from various positions around it.
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In order to plot the points from the hypergraph onto a sphere (the first step before converting to a Mollweide projection), the coordinates of the center-most node was set to be the origin, and the coordinates were converted to spherical coordinates, and from there I was able to derive the
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Concluding Remarks
With the hypergraph mapped to a Mollweide projection, the next step would be to create a heat map of the points (which has already been toyed with, albeit not perfected), and create a fully visualised cosmic microwave background for this notable universe. With the functions created, this process can be repeated multiple times for various hypergraphs, in hopes that perhaps we will become closer to finding a model of our universe.
Keywords
Wolfram High School Summer Camp
◼
Wolfram Language
◼
POSTED BY:
Macy Maurer Levin
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Anwesha Das
Anwesha Das, Delhi Public School Kalyanpur
Posted
10 months ago
Macy! So great to see you attend WSC again. Awesome project!
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Anwesha Das
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Macy Maurer Levin
Macy Maurer Levin, Stanford OHS
Posted
9 months ago
thank you! :)
POSTED BY:
Macy Maurer Levin
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