Hypergraph Universe 2D — Emergent Spacetime Dimension

Instead of starting from space and placing particles in it, this simulation starts from nothing but a small graph and a local rewriting rule — an idea explored seriously in "digital physics" and the Wolfram model of fundamental physics. Watching the graph unfold in 2D, space itself seems to appear: distance, neighbourhoods and even a measurable dimension all emerge purely from how the graph's connectivity grows, with no coordinates ever written into the rule. A live breadth-first-search dimension estimate — plotted as a log-log ball-growth curve alongside the graph — shows this "emergent geometry" as a single number that updates as the universe grows.