Billiards with Spatial Memory

Mathematical billiards with self-avoiding particles are studied. The particles self-trap and show chaotic motion (see Figure 1 of the pre-print and the dataset here). In a triangular billiard, the self-trapping locations form a complex pattern with a wide long-tailed distribution of trajectory lengths (see Figure 2 of the pre-print and the dataset here). The final pattern depends on the geometry of the polygon (see Figure 3 of the pre-print and the dataset here). Each subfolder includes the description of the raw data. Link to Pre-print: https://arxiv.org/abs/2307.01734