Fractals: An Eclectic Survey, Part II

Abstract

Fractals are geometric shapes and patterns that can describe the roughness (or irregularity) present in almost every object in nature. Many fractals may repeat their geometry at smaller or larger scales. This paper is the second (and last) part of a series of two papers dedicated to an eclectic survey of fractals describing the infinite complexity and amazing beauty of fractals from historical, theoretical, mathematical, aesthetical and technological aspects, including their diverse applications in various fields. In this article, our focus is on engineering, industrial, commercial and futuristic applications of fractals, whereas in the first part, we discussed the basics of fractals, mathematical description, fractal dimension and artistic applications. Among many different applications of fractals, fractal landscape generation (fractal landscapes that can simulate and describe natural terrains and landscapes more precisely by mathematical models of fractal geometry), fractal antennas (fractal-shaped antennas that are designed and used in devices which operate on multiple and wider frequency bands) and fractal image compression (a fractal-based lossy compression method for digital and natural images which uses inherent self-similarity present in an image) are the most creative, engineering-driven, industry-oriented, commercial and emerging applications. We consider each of these applications in detail along with some innovative and future ready applications.

Study of Diminutive Antenna employing identical elliptical notch in Elliptical Microstrip patch for multiband applications

“…The primary objective of the generally utilised techniques to attain a multiband echoing frequency is the multiband microstrip antenna. Numerous methods, as drilling slots into the antenna's metallic components or employing multiple transmitting portions, have been suggested to build multiband antennas [4,[6][7][8][9][10][11]. Multiband antennas offer several benefits over traditional antennas in a comparable class.…”

Fractal Dimensions of Biomass Burning Aerosols from TEM Images Using the Box-Grid and Nested Squares Methods

“…The fractal dimension is a decimal value that denotes the complexity of fractal, geometric shapes possessing self-similarity, such as the BB aerosols. The study of fractals occurs in a multitude of fields ranging from the study of root systems to image compression to the study of particulate matter in the atmosphere [37,38]. In this study we differentiate fractal dimension values by whether they were obtained by directly measuring the threedimensional aerosol" by directly calculating the three-dimensional fractal dimensions using Eq.…”

Fractal Parameters as Independent Biomarkers in the Early Diagnosis of Pediatric Onset Inflammatory Bowel Disease

“…Amongst other descriptors, fractal-based parameters have been used with success. As pointed out in [1], many natural and man-made objects can be characterized using the classical geometry and integer dimension; however, the random growth and/or branching of natural objects, at different scales, can be described in a sufficiently precise and concise way only by means of a non-integer fractal dimension. Some of the representative examples include a fern leaf, the branching in human lungs, a broccoli head, and the electric discharge in a storm [1].…”

“…In fractal objects, self-similarity at varying scales can be observed. Applications of fractal analysis to biomedical problems have been well established in ophthalmology, in exhibiting the fractal structure of vascular networks, and in the study of branching patterns of nerve dendrites, as well as in the studies of altered tissue and cell characteristics in cancers [1][2][3][4][5][6].…”

“…Fractal Fract. 2023, 7, 619 2 of 16 The dependences of the structural or functioning-related parameters of interest on the scale can be expressed by the power-law equations [1,7,8]. The fractal dimension (FD), which corresponds to the first-order mass moment of probability of finding a certain fractal measure amount at a certain scale [9,10], can be easily determined from the power-law dependence.…”