I've been independently investigating a specific graph based substitution system I call the Space Element Reduction Duplication (SERD) network for several years now. I see many connections with the Wolfram Model and so I thought it would be right to publicise my research here and hopefully start some discussion on the subject.
It was the subject of my theoretical physics masters thesis and research project at the 2015 Wolfram Summer school. (You can probably find my project on the alumni page if you're interested.) Since then I've published two papers, one in Journal of Cellular Automata, and one in Complex systems and the system has definitely developed a lot since then.
Despite producing two papers on the subject, I have had very little feedback or collaboration on the system since the summer school and thought that this would be a great way to reconnect my research with the Wolfram physics community. In my papers I did not include any of the source code that I used for my experiments and so that is what I am publishing here. I am sure my code is likely not very efficient, I'm not an expert coder, (a consequence of working independently I suppose) but it works and you are welcome to investigate it in all of its gory detail and implement it yourself.
In essence, the rules and structure of this system emerge out of a philosophical idea concerning why the universe exists, the existence of nothingness and planes of dimensions within nothingness. You end up with a highly dynamic network structure, where information propagates through its edges and is updated on vertices that act as both massive particles and as observers of the system.
Anyway, I've provided a link to a Mathematica notebook that acts as an introduction to the system, a code repository and provides results from some experiments that I have done recently. I've been testing for compatibility with Newtons laws and special relativity and I think I've got some interesting results. I do have many other results and also ideas for future experiments on this system. I've also provided links to a Youtube series that I have made where I describe my research, as well attaching my two published papers and two additional self published papers for additional material if anyone is interested. The system has developed a lot over the years and so just bare in mind that some of the older material may now be a little outdated
Introductory Mathematica notebook and code repository: https://drive.google.com/file/d/1rVrR7z73NAdIk1JKtp-BnWedeKJNgQuo/view?usp=sharing
Youtube series: Video 1: A qualitative introduction - https://youtu.be/35MkO2p7yV8 Video 2: An introduction to the code and some results - https://youtu.be/BPQi0WfGMRs Video 3: Demonstration of compatibility with Newton's laws - https://youtu.be/KZEO-ZHGgPM Video 4.1: Evidence of constancy of speed of light in all inertial reference frames - Part 1 - https://youtu.be/yr6hwaz8Hkk Video 4.2: Evidence of constancy of speed of light in all inertial reference frames - Part 2 - https://youtu.be/rhwWCyaJvDY
Let me know what you think about the system, any gaping holes in it, or things you may like. Whether or not it is a representation of the universe, I think it's a very beautiful, intricate and elegant system that I would love to explore more of, even if it is not fully physically comparable. Perhaps it may lead to some interesting insights that we do not yet know of. Feel free to ask me any questions about the system or the philosophical motivation. The rules are pretty concrete and should speak for themselves even if I've made some small slip ups in my own representation of the system.
If you can think of any research groups that it may be worth reaching out to, for whom this research would be of interest to, do let me know. That would be very useful as I've been doing most of this research purely independently and off my own back, and could really do with some outside perspective and/or collaboration on this project.
