Fractal-Thermodynamic System Analogy and Complexity of Plant Leaves

Jaishanker³

2023

Preprint

Self Cite

Shape is an objective characteristic of an object. A boundary separates a physical object from its surroundings. It defines the shape and regulates energy flux into and from an object. Visual perception of a definite shape (geometry) of physical objects is an abstraction. While the perceived geometry at an object's sharp interface (macro) creates a Euclidian illusion of actual shape, the notion of diffuse interfaces (micro) allows an understanding of the realistic form of objects. Here we formulate a dimensionless geometric entropy of plant leaves (SL) by a 2-D description of a phase-field function. We applied this method to 109 tropical plant leaf images. SL was estimated from the leaf perimeter (P) and leaf area (A). It correlates positively with a fractal dimensional measure of leaf complexity, viz., segmental fractal complexity. Leaves with a higher P: A ratio has higher SL and possesses complex morphology. The univariate cluster analysis of SL reveals the taxonomic relationship among the leaf shapes at the generic level. An increase in SL of plant leaves could be an evolutionary strategy. The results of morphological complexity presented in this paper will trigger discussion on the causal links between leaf adaptive stability/efficiency and complexity. We present SL as a derived plant trait to describe plant leaf complexity and adaptive stability. Integrating SL into other leaf physiological measures will help understand energy dynamics and information flow in ecological systems.

Section: Discussionmentioning

confidence: 74%

“…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.…”

Section: Dataset and Measurementmentioning

confidence: 99%

Geometric Entropy of plant leaves: A measure of morphological complexity

Jaishanker³

2023

Preprint

Self Cite

“…SL was correlated with Segmental Fractal Complexity (DΣS) (Vishnu and Jaishanker 2022). DΣS is an enhanced fractal measure constituting the fractal dimensions of leaf image parts, viz., leaf lamina, the background, and leaf edges.…”

Section: 1datasetmentioning

confidence: 99%

Geometric Entropy of Plant Leaves: A Measure of Morphological Complexity

Jaishanker

2022

Preprint

Self Cite

A boundary separates a physical object from its surroundings. It defines the object's shape and regulates energy flux to and from it. Visual perception of the shape (geometry) of physical objects is an abstraction. While the perceived geometry at an object's sharp interface (macro) creates a Euclidian illusion of actual shape, the notion of diffuse interfaces (micro) allows grasping the realistic form of objects. Here we formulate a dimensionless geometric entropy of plant leaves (SL) by a 2-D description of a phase-field function. SL is estimated from the leaf perimeter (P) and leaf area (A) and correlates positively with segmental fractal complexity (DΣS). Leaves with a higher P:A ratio has higher SL and morphological complexity. An increase in SL of plant leaves could be an evolutionary strategy. The results of morphological complexity presented in this paper will trigger discussion on the causal links between leaf adaptive stability/efficiency and complexity. We present SL as a derived plant trait to describe plant leaf complexity and adaptive stability. Integrating SL into other leaf physiological measures will help understand energy dynamics and information flow in ecological systems.

Geometric Entropy of Plant Leaves: A Measure of Morphological Complexity

Jaishanker³

2022

Preprint

A boundary separates a physical object from its surroundings. It defines the object's shape and regulates energy flux to and from it. Visual perception of the shape (geometry) of physical objects is an abstraction. While the perceived geometry at an object's sharp interface (macro) creates a Euclidian illusion of actual shape, the notion of diffuse interfaces (micro) allows grasping the realistic form of objects. Here we formulate a dimensionless geometric entropy of plant leaves (SL) by a 2-D description of a phase-field function. SL is estimated from the leaf perimeter (P) and leaf area (A) and correlates positively with segmental fractal complexity (DΣS ). Leaves with a higher P:A ratio has higher SL and morphological complexity. An increase in SL of plant leaves could be an evolutionary strategy. The results of morphological complexity presented in this paper will trigger discussion on the causal links between leaf adaptive stability/efficiency and complexity. We present SL as a derived plant trait to describe plant leaf complexity and adaptive stability. Integrating SL into other leaf physiological measures will help understand energy dynamics and information flow in ecological systems.