Determining the limits of traditional box-counting fractal analysis in leaf complexity studies

Abstract

Fractal-based measures have widespread applications in the characterization of complex biological structures. Box-counting is one of the most widely used methods of fractal analysis. However, the utility of traditional box-counting fractal analysis in complexity studies is limited. We discuss the shortfalls of traditional fractal dimension (D) approaches in leaf complexity studies. Mature and healthy flat leaves of 61 plant species were collected from Trivandrum, Kerala, India. Digital images of these leaves were analyzed using the ImageJ software. No significant variations in D were seen in the results that could differentiate the leaf forms. We present the limitations and biases affecting accurate D analysis. Fractal properties of plant leaves are restricted over a limited scale, causing the failure of the linear regression-based D estimates. Arbitrary grid placement and miscounting the boxes of a specific size to cover the leaves are also subject to quantization errors. Since traditional fractal analysis depends on the bulk and boundary of the leaves, some D errors result from the potential bias of this area dependency. The traditional box-counting analysis also fails to capture the lacunarity observed in leaf images. Hence an accurate estimation of D is challenging using conventional methods. Considering the broad utility of fractal methods, plant researchers must be sensitized about the uncertainties in traditional box-counting approaches in complexity studies.