Causal Dynamical Triangulation: Spacetime Built from Simplices

Quantum gravity's central puzzle is that spacetime itself should be quantum — fluctuating, discrete at the smallest scales, yet smooth and four(or here, two)-dimensional on average. Causal dynamical triangulation (CDT) answers this by literally building spacetime out of flat triangular building blocks glued edge-to-edge, one causally-ordered time slice at a time, and then summing over every way that gluing could have happened. This simulator renders a real 2D CDT lattice — a stack of discrete spatial circles connected by simplices whose count follows the actual mean volume profile found in CDT path-integral simulations — and lets you run a genuine diffusion experiment on it: launch random walkers across the simplicial graph and extract the spectral dimension from their return probability, the same technique physicists use to show that quantum spacetime can look lower-dimensional at short distances than it does at long ones.