Fractal-Thermodynamic System Analogy and Complexity of Plant Leaves

Abstract

More precise measurements of the complexity of leaf shapes can open new pathways to understanding plant adaptation and resilience in the face of changing environments. We present a method to measure the complexity of plant leaf shapes by relating their fractal dimensions to topological entropy. Our method relies on segmental fractal complexity and stems from a fractal-thermodynamic system analogy. The complexity of plant leaf shapes is an algebraic combination of the fractal dimensions of the components of the leaf-image system. We applied this method to leaf forms of 30 tropical plant species. While topological entropy is positively correlated with the leaf dissection index, it is an improvement over the leaf dissection index because of its ability to capture the spatial positioning of the leaf lamina, the leaf edges, and the leaf background. The topological entropy method is also an advancement over conventional geometric and fractal dimension-based measures of leaf complexity because it does not entail information loss due to the pre-processing and is perceptibly simple.