1. Introduction

A fractal structure is a never-finishing pattern. These structures are infinitely complex patterns that are self-similar across diverse scales [1]. Due to this self-similar performance, fractals find diverse applications in both science and engineering. The word fractal has its origin in the Latin word fractus, meaning an irregular surface. Coastal line of sea, mountains, sea shells, snowflakes, leaves and eye strain of a peacock are some of the naturally existed fractals [2].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Figure 1 shows some of the naturally existed fractals in the nature. By their geometrical constructions, fractal patterns come in two main variations:


All natural fractals come under random fractals because they do not have a particular deterministic way of generation and they are non-integral surfaces. These are also known as stochastic fractals. The generation of these fractals is analysed by different statistical techniques. The randomness of these fractals varies with structure to structure and way of generation. The Brownian motion of microscopic particles in fluid is also the best example for random fractal behaviour as shown in Figure 2. Deterministic fractals are geometry-based structures having scaled repetitive nature. These fractals have exact dimensions for the expansion unlike random fractals. Generally, all deterministic fractals are generated using iterated function system (IFS), recurrent iterated function systems (RIFS) and complex number methods. In these methods of

generation, fractal structures are created on the source of scaling, plan axis rotation and dislocation. The most popular IFS and complex number fractals are the Koch curve, the Sierpinski triangle, Julia sets and the Sierpinski square which are shown in Figure 3. In these deterministic fractal structures, the basic generator or seed is copied itself up to infinite iterations (p) [3–5]. The design methodology proposed in this chapter for the generation of various fractal array antennas

Fractal Array Antennas and Applications http://dx.doi.org/10.5772/intechopen.74729 15

Fractal geometric technology has permeated numerous areas of science and engineering, such as astrophysics, image processing, biological sciences, bioinformatics, antenna engineering,

• Image compression using fractal image coding has led to a major fall in memory requirements and processing time than conventional techniques [6]. Figure 4 exemplifies the process of fractal image compression. The output images of shape 'A' unite to the Sierpinski triangle. This last image is called 'attractor' for this photocopying mechanism. Any original image will be transformed to the attractor if the mechanism runs repetitively.

• The fractal structures inspired from the human blood vessels of fractal nature offer an easy low-pressure network to achieve a silicon chip to allow a cooling fluid to uniformly flow

• The human body is also having fractal nature. The DNA, retina, blood vessels and lobes of the lungs are self-similar structures. Euclidean geometry is powerless to study and

This characteristic is the advantage to the fractal image compression.

across the surface of the chip, and this keeps the computer cool.

is also having a deterministic way of generation.

Figure 2. The Brownian motion of microscopic particles.

computer graphics and medical applications:

2. Applications of fractals

Figure 1. (a) Eye strain of a peacock. (b) Fractal-shaped leaf.

Figure 2. The Brownian motion of microscopic particles.

Figure 1 shows some of the naturally existed fractals in the nature. By their geometrical

All natural fractals come under random fractals because they do not have a particular deterministic way of generation and they are non-integral surfaces. These are also known as stochastic fractals. The generation of these fractals is analysed by different statistical techniques. The randomness of these fractals varies with structure to structure and way of generation. The Brownian motion of microscopic particles in fluid is also the best example for random fractal behaviour as shown in Figure 2. Deterministic fractals are geometry-based structures having scaled repetitive nature. These fractals have exact dimensions for the expansion unlike random fractals. Generally, all deterministic fractals are generated using iterated function system (IFS), recurrent iterated function systems (RIFS) and complex number methods. In these methods of

constructions, fractal patterns come in two main variations:

14 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

1. Random fractals

2. Deterministic or geometric fractals

Figure 1. (a) Eye strain of a peacock. (b) Fractal-shaped leaf.

generation, fractal structures are created on the source of scaling, plan axis rotation and dislocation. The most popular IFS and complex number fractals are the Koch curve, the Sierpinski triangle, Julia sets and the Sierpinski square which are shown in Figure 3. In these deterministic fractal structures, the basic generator or seed is copied itself up to infinite iterations (p) [3–5]. The design methodology proposed in this chapter for the generation of various fractal array antennas is also having a deterministic way of generation.
