Why Cracks and Cells Meet at 120 Degrees
Dried mud, cooling basalt columns and a giraffe's coat pattern all split into cells whose cracks meet at close to 120 degrees. Measure the angle in a real photograph and model why that number appears.
Introduction
Cracks in drying mud, the hexagonal basalt columns of the Giant's Causeway, and the patches on a giraffe's coat all form roughly polygonal cells, and the corners where three cracks or cell walls meet are close to 120 degrees rather than a random angle. This is the same angle that appears where three soap-film walls meet in a foam, because it is the arrangement that minimises total crack (or wall) length for a given area. This exploration asks you to photograph or find a real cracked or cellular surface, measure the angles at its junctions, and test whether they cluster near 120 degrees, then model why that particular angle is favoured.
Guiding Questions
- Find or take a photograph of a cracked or cellular surface (dried mud, basalt columns, a giraffe's coat, a soap-bubble raft) and measure the angles where three edges meet at several junctions.
- Do your measured angles cluster around 120 degrees? How much do they vary, and what might explain the variation?
- Model a simple network of cells and show why 120-degree junctions minimise the total length of the cell walls for a fixed enclosed area.
- Compare your real surface with an idealised hexagonal tiling. Where does the real pattern match the model, and where does it break down?