The simplified idea taken from Stephen Wolfram's book "Project to find the fundamental theory of physics" is that our universe could be represented with a (hyper)graph. Moreover, time is just some one universal rule that is applied to the graph every "Planck time" (discrete time required) which stays constant for the duration of all of time.

This might seem strange, but if we would say that every single quark in the universe is a vertex and all fundamental forces are (hyper)edges between quarks or something, it becomes more plausible, we just need an absolutely insanely large (hyper)graph.

Another way to look at this is that a graph with some set of graph rewriting rules is a sort of a grammar and is Turing complete. Seeing that, the fundamental argument here is just that the universe can be simulated on a computer.

The "Universal rule" is just graph rewriting as I said, it is a function that takes in (hyper)edges and outputs some reconfiguration of the inputted (hyper)edges possibly with new vertices. Two examples:

Rule ([X,Y],[X,Z]) -> ([Y,X],[Z,X]) finds all vertices that connect to two other vertices and simply reverses edges in question. For example in the following graph, edges ([3,1],[3,4]) get pattern matched in our rule and ([1,3],[4,3]) is outputted so those two edges get affected.

In the next iteration of the rule, edges ([1,2],[1,3]) and ([4,1],[4,3]) would be affected.

Much more interesting are rules that add a new vertex, for example Rule ([X,Y],[X,Z]) -> ([X,W],[W,Y],[X,Z])

Here it is again applied to our graph, again, the left side of the rule pattern matches and the right side describes the new configuration.

And thats it! Rules can act on completely disconnected parts of the graph, for example ([X,Y], [U,V]) on the left side of a rule would just pattern match with any pair of edges.

Usage:

nSteps rule2 rule2_params universe_singularity 4

This applies the rule2 defined in the file to the universe singularity 4 times in a row. Replacing 4 with a sufficiently large number and defining an appropriate rule to replace rule2 should result in simulating our universe. Run the experiment at your own risk, if intelligent life emerges, do NOT interrupt the simulation :).