Evolution of SERD network under observation with time iterated strain minimization embedding.

These simulations show the evolution of an ensemble of microstate paths for 20 time steps evolving from a single microstate path of 80 time steps which then repeats. What is observed is the ensemble. This allows for a single microstate to evolve much further and then be studied by taking expectation values from ensembles of possible paths after a certain point.
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.
In this specific example a strain minimization algorithm is applied at each time step to determine the new coordinatization of the system at that moment in time. Also in each timestep the space elements constructing the edges of the graph may duplicate or reduce causing the state graph to evolve. The information of these duplications and reductions propagates through the dynamic graph and updates the state of the system when the information reaches the centralized point particle at the origin.
The number of point particles in each evolution is given by the number of lines one the graph. For each run it is constant and so no point particle splitting occurs.
The graphs show the evolution of the expectation values of the instantaneous velocities of each of the point particles in the system. Notice how when velocities are above one they drop down and when they are below one they tend up to one.
This is one promising physically comparable behaviour of the SERD system, point particles tend to velocity of below 1 space element per timestep. Whenever the velocities go above one there appears to be a recoil back to one. Initially the state is observed, this is a very extreme condition and as the state relaxes the velocity appears to tend back to one. Since point particles constitute all massive particles within this system, this is some very preliminary evidence of relativistic behaviour. Taking the space element and the time step to be approximately the plank length and plank time respectively, this corresponds to the light speed limit on massive particles.
The large velocities occur in the first two timesteps but this is still not incompatible with physics as this is the moment where the wavefunction collapses and so may lead to non-local behaviour, in this case it may be explained by point particles tunnelling outside a potential well.
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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