WHAT IS A FRACTAL different scales. This property is called “ Fractals are extremely complex, sometimes infinitely complex - meaning you can zoom in and find the same shapes forever. …

In this book, we study fractals as they arise in pure mathematics, focusing on the computational aspects of the subject. Figure 1.1 suggests the flavor of the subject. While different in appearance, these …

Fractal-shape antennas can respond to more frequencies than regular ones. They can be 1⁄4 the size of the regular ones: use in cellular phones and military communication hardware. BUT: Not all fractal …

Definition A fractal is a subset of Rn that is self similar and whose fractal dimension exceeds its topological dimension. Now we need to discuss the concepts that are involved in this definition. The …

The Koch curve is self-similar in that it comprises N = 4 copies of itself shrunk by a factor of r = 3. 1 Its fractal dimension is therefore log4 log3 ≈ 1.2619, between that of a line and an area.

The study of fractals from a mathematical point of view first began with Benoit Mandelbrot’s seminal work entitled The Fractal Geometry of Nature, published in 1982.

Fractal geometry is used to model natural phenomena characterised by irregularity and self-similarity, such as coastlines, clouds, mountains, and biological structures.