Image Courtesy: Wired.
When natural objects break down, what basic structure do the pieces tend to attain? Is there a universal basic structural entity that natural objects tend to fragment into? From microscopic to planetary, can there be a universal rule of object fragmentation?
These are questions that Professor Gabor Domokos of Budapest University of Technology and Economics has been trying to answer for some time now. The latest paper, published by his team in the peer-reviewed multidisciplinary scientific journal Proceedings of the National Academy of Sciences (PNAS), suggests that there may exist a universal rule of fragmentation of natural objects, and that fragments tend to acquire the shape of a cube as a basic structure.
In 2006, Domokos mathematically proved the existence of gomboc, a gemstone-like shape. A gomboc has only one stable balancing point – it will come to rest in a particular position regardless of how it is placed on a plane. A cylinder, for example, can rest in two directions—either on its end or its side, but gomboc has only one such point. Domokos and his colleagues subsequently found that objects like pebbles and sand grains tend to fragment into the shape resembling a gomboc, but don’t ever achieve the ideal state. According to Domokos, the gomboc shape is a part of nature.
In the latest PNAS paper the group created supercomputer-simulated modelling of the break up of three-dimensional materials; what happens when a rock is pulled equally in all directions, for example. In such cases, they found that objects tend to break up into polyhedral pieces – cubes, on an average.
Earlier, the team studied the fragmentation of a cube. They again used computer simulation and sliced the cube with 50 two-dimensional planes which were inserted at random angles. The planes cut the cube into six lakhs fragments. Interestingly, the fragments were cubic. This result led the researchers to speculate that cube might be a basic structure that fragmentation can give rise to.
To test their computer simulated results on real world objects, the researchers subjected mineral dolomite from the mountains in Budapest to the process and counted the number of vertices in the cracks in the faces of the stones. They found that most of the cracks were of a squarish shape. The squarish shape is one of the faces of a cube; they found this regardless of whether the stones weathered naturally or when created by humans when dynamite was used on the mountain.
However, there are certain issues. Minerals such as mica fragment into flakes and there are other minerals which do not obey the cubic shape theory. Douglas Jerolmack, a co-author of the paper told Science Magazine that it was because real materials are not found in ideal forms as those used in their simulations. “But in a statistical averaged sense, rocks are born as something that’s a vague shadow of a cube,” he was quoted saying.
Jeromack also said that the results were more philosophical than scientific. The inspiration that drove the team was Plato. Plato imagined four classical elements – earth, air, fire, water – to be linked to a regular polyhedron and linked the earth with a cube. A cube is a platonic object and is a special kind of a polyhedron, which has all faces the same.
“We demonstrate that this idea is essentially correct: Appropriately averaged properties of most natural 3D fragments reproduce the topological cube. We use mechanical and geometric models to explain the ubiquity of Plato’s cube in fragmentation and to uniquely map distinct fragment patterns to their formative stress conditions,” the authors wrote in their PNAS paper.