A new mathematical study explains why broken objects tend to produce a familiar mess of fragments rather than neat pieces, tells this interesting article from Live Science. French physicist Emmanuel Villermaux developed an equation based on a principle he calls maximal randomness, which says that when something shatters, the most likely outcome is the one with the greatest disorder, or entropy. But pure randomness isn’t enough on its own. To turn that idea into a predictive formula, Villermaux combined it with a conservation law discovered in 2015 that limits how many fragments can occupy space after breakage. Together, these two ideas produce a universal mathematical description of how fragments of different sizes are distributed when an object breaks.
The equation doesn’t describe the exact paths of cracks or how they start, but it captures an overall pattern seen across materials. When researchers compared its predictions to decades of fragmentation data, from shattered glass and broken pasta to exploding bubbles and dry sugar cubes, the predicted mix of large, medium, and tiny fragments lined up with real outcomes. Villermaux also tested the formula with simple experiments, such as dropping heavy objects onto sugar cubes and measuring the pieces, and found a close match.
This law has limits. It doesn’t work for breakage that is orderly or uniform, like water forming equal-sized droplets, or in materials where fragments interact strongly after breaking, as in some plastics. But in many everyday cases of chaotic shattering, such as a vase falling off a shelf, the principle of maximal randomness explains why the pattern of fragments looks so unpredictable yet still follows a consistent rule.
Understanding this rule could help scientists and engineers predict fragment size in industrial and geological contexts, such as mining or rockfalls. Future research may look at the smallest possible fragment sizes and whether the shapes of shards follow similar patterns.