Evolution of internal geometry of single microstate path of SERD system. 8 point particles. #3

These simulations represent sequential evolutions of a single microstate path within the SERD network.
The SERD network, or Space Element Reduction Duplication network, is a discrete dynamic system that emerges out a philosophical principle relating to the universes existence and has shown some interesting, potentially physically comparable behaviour.
Each frame represents the observed geometry of an individual state when embedded, in this case, in two dimensions. A state can be represented as a complete graph, with positive integer edge weights. The edge weights correspond to a metric distance measure.
When the vertices or point particles (PPs) are coordinatized this induces Euclidean violations, which can be represented as strain within the edges that exerts a force on the corresponding PPs. A strain minimization algorithm may be used to find a coordinatization that minimizes the internal strain and therefore the geometric curvature. A trace of this geometry is produced by choosing random initial coordinates and then iteratively relaxing these coordinates into their strain minimized configuration with the strain minimization algorithm.
The dark spots correspond to where points are close together, therefore the points have a smaller iterative displacement and so correspond to areas of lower net strain whereas the lighter areas correspond to areas with larger net strain since there is a larger particle displacement.
The symmetries of the embedding correspond to the fixing of the centralised point particle (vertex at the origin) and the second coordinate orientation point particle on the x axis. As a result each configuration may be reflected in each axis giving the two lines of symmetry along the x and y axes.
If you are interested in any of these systems or want to find out more check out some of my papers on my academia page.
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Space Element Reduction Duplication network as a good starting point, but if you want a more technical description you can look at my two published papers on the subject.
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I’m really interested to hear any feedback or if anyone would like to simply discuss some of the details of system, that I am investigating. I would be very happy to do that.
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