Critical fragmentation properties of random drilling: How many random holes need to be drilled to collapse a wooden cube?

TL;DR

This paper investigates the fragmentation of a wooden cube under random drilling, revealing complex geometrical and probabilistic behaviors, including a critical transition point that differs from classical percolation theory.

Contribution

It combines numerical simulations and rigorous analysis to uncover the critical fragmentation behavior and scale-free properties in the process.

Findings

Identification of a critical hole density for cube collapse

Discovery of off-critical scale-free fragmentation behavior

Demonstration of a continuous transition differing from classical percolation

Abstract

A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical and probabilistic behavior that is discussed here. Combining numerical simulations and rigorous results, we find off-critical scale-free behavior and a continuous transition at a critical density of holes that significantly differs from classical percolation.