What is going on here? Well what I want to try and do initially is generate random discrete spaces, triangulate them and calculate their properties using simplex complexes based on tetrahedra.
As starting point I am using Sage to generate a pointset of 20 random points which is then triangulated and plotted in 3d.
There are several research routes I can consider following on from this:
- Specialise down to random tetrahedra – then quantise and calculate their area and volume spectra.
- Implement pachner moves and measure how properties such as local energy and curvature vary with triangulation.
- Convert to spin network, then spinfoam and investigate at how 4d spacetimes could be generated – comparing results with findings of Causal Dynamical Triangulations of Ambjørn Jurkiewicz and Loll.