Hypergraph Universe 2D: A Model of Emergent Spacetime Dimension

What is Hypergraph Universe 2D?

Hypergraph Universe 2D is a digital physics model where a two-dimensional directed graph evolves over time through a local rewriting rule. This rule, inspired by the Wolfram model framework, dictates how nodes and edges are added or modified according to specific patterns. The emergent properties of this evolving structure can be used to infer the dimensionality of the underlying space.

The live breadth-first-search ball-growth plot provides real-time feedback on the spatial dimension of the graph as it grows, offering insights into how complex structures can arise from simple initial conditions and local rules.

How Does It Work?

At each step, a node in the hypergraph is selected based on its hop distance or degree. This node then undergoes a rewriting rule that transforms it into a new configuration of nodes and edges. The process continues iteratively, leading to an expanding graph that can be visualized as a growing structure.

The breadth-first-search ball-growth plot tracks the expansion of the graph by simulating the spread of information from a central node. This helps in estimating the emergent spatial dimension of the hypergraph universe, providing a dynamic and interactive way to explore the concept.

Why Does It Matter?

The study of Hypergraph Universe 2D is significant because it offers a computational model for understanding the emergence of spacetime from fundamental principles. This approach can help in formulating theories about the nature of reality at its most basic level, potentially bridging the gap between quantum mechanics and general relativity.

Moreover, this model provides a new perspective on how complex structures can arise from simple rules, which has implications for fields such as computer science, network theory, and even philosophy.

Real-World Applications

The insights gained from Hypergraph Universe 2D could be applied to the development of new algorithms in machine learning and artificial intelligence. Understanding how complex networks form can also aid in designing more robust and efficient communication systems.

Additionally, this model may contribute to the theoretical foundations of quantum gravity and cosmology, offering a novel way to explore the origins and evolution of the universe.

Frequently asked questions

Try it live

Everything above runs in your browser — open Hypergraph Universe 2D — Emergent Spacetime Dimension and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.