Abstract: The project is concerned with discovering correlations between the growth of dimensionality of the model with the number of steps applied. The first step is to categorize the rules based on whether they lead to increasing, decreasing or periodic relationships with the number of dimensions. Based on that information, it may be possible to study the connection to particle physics - to explore how the de Sitter entropy of the universe relates to the entropy of the graph. The results will also be relevant to study the correspondence between the evolution of the Wolfram models and early universe inflation models - to analyze the evolution of the quantum degrees of freedom as the universe was expanding.
​​
​Main findings: classification of the rules based on the value of the slopes of their dimensionality graph approximations; alternative approach to dimensionality approximation, distributions of the universes based on their stability. ​
​
​Next steps: Exploring other signatures, getting a larger set of results for the initial condition variance for the spectral dimension.

Variable
​There are three variables that we can vary:
- the initial conditions of the hypergraphs based on the signature;
- the update rules based on the signature;
- the way that the rules are applied, i.e. least recent edge/random.
​
Here,we only work with the first two, i.e.explore the variation with the initial conditions as well as the variation with different rules.
​
Let’s begin with a demonstration of the approach on the classic example.

Example