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 global changes. We present a method to measure the complexity of plant leaf shapes by relating their fractal dimension 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 dimension of the components, leaf lamina, background, and leaf edge. We applied this method to leaf forms of 42 tropical plant species. Topological entropy is an improvement over the leaf dissection index because of its ability to capture the spatial positioning of a leaf's lamina, edge, and background. It 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.

Geometric entropy of plant leaves: A measure of morphological complexity

“…The ease of use and efficiency of S L will encourage plant biologists to draw more accurate inferences on leaf shape variations. Moreover, the theoretical maximum of D ΣS of extremely narrow leaves and the Peano curve-shaped leaves with a high P/A ratio [ 47 ] consolidates S L . Since complex leaves (high P/A ratio) have more adaptive stability in changing environments [ 80 , 81 ], S L can be considered a derived plant trait to describe leaf complexity and adaptive stability.…”

“…Segmental fractal complexity ( D ΣS ) is an improved leaf complexity measure from a fractal-thermodynamic system analogy [ 47 ]. It is an algebraic combination of the fractal dimensions of the components of the leaf images, viz., leaf lamina, the background, and leaf edges.…”