Fractal structures and mechanical properties of ammonite shells

Abstract

The fractal structure of the blade-type lines of shells of extinct forms of ammonites of various types is investigated. These lines correspond to the connecting seams between the previous and new chambers that the mollusc builds during its gradual growth. Evolutionarily older forms have nearly straight or wavy seams with low tortuosity (the ratio of line length to end-point distance). Over the course of evolution, the shape of these lines has become more complex and acquired fractal properties, so that evolutionarily new types have connecting seams of a very complex shape. The fractal dimensions Df of the blade lines were measured using the box-counting method. It was shown that the fractal dimensions of the lobed lines of shells of different evolutionary ages increase from Df= 1.1 to Df = 1.9. In addition, with an increase in the chamber number, the Df values increase and remain larger on the outer surface of the chamber than on the inner one. The relationship between the fractal structure and an increase in the mechanical strength of the weld is discussed.