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.

Keywords

• fractals
• iterated function system
• fractal landscapes
• fractal antenna
• fractal image compression
• fractal batteries