Universal fluctuation of polygonal crack geometry in solidified lava

TL;DR

This study reveals that the shape variation of polygonal cracks in solidified lava follows a universal Gumbel distribution, suggesting a common underlying process across different localities and compositions.

Contribution

It uncovers a universal statistical law governing polygonal crack shapes in lava, linking them to a broader class of fractured brittle materials.

Findings

Polygonal crack shapes follow a Gumbel distribution.

The distribution is consistent across different localities and compositions.

A universal class for polygonal crack networks is proposed.

Abstract

Outcrops of columnar joints made of solidified lava flows are often covered by semi-ordered polygonal cracks. The polygon diameters are fairly uniform at each outcrop, but their shapes largely vary in the number of sides and internal angles. Herein, we unveil that the statistical variation in the polygon shape follows an extreme value distribution class: the Gumbel distribution. The Gumbel law was found to hold for different columnar joints, regardless of the locality, lithologic composition, and typical diameter. A common distribution for columnar joints implies a new universal class that may integrate the polygonal crack networks observed on the surface of various fractured brittle materials.