Fractals play an important role in modeling natural phenomena and engineering processes. And fractals have a close connection to the concepts of chaotic dynamics. This monograph presents definitions, concepts, notions and methodologies of both spatial and temporal fractals. It addresses students and researchers in chemistry and in chemical engineering. The authors present the concepts and methodologies in sufficient detail for uninitiated readers. They include many simple examples and graphical illustrations. They outline some examples in more detail: Perimeter fractal dimension of char particles, surface fractal dimension of charcoal; fractal analysis of pressure fluctuation in multiphase flow systems. Readers who master the concepts in this book, can confidently apply them to their fields of interest.

Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.

Historically, science has developed by reducing complex situations to simple ones, analyzing the components and synthesizing the original situation. While this 'reductionist' approach has been extremely successful, there are phenomena of such complexity that one cannot simplify them without eliminating the problem itself. Recently, attention has turned to such problems in a wide variety of fields. This is in part due to the development of fractal geometry. Fractal geometry provides the mathematical tools for handling complexity. The present volume is a collection of papers that deal with the application of fractals in both traditional scientific disciplines and in applied fields. This volume shows the advance of our understanding of complex phenomena across a spectrum of disciplines. While these diverse fields work on very different problems, fractals provide a unifying formalism for approaching these problems.

This text features 105 papers dealing with the fundamentals and the applications of poromechanics from the Biot conference of 1998, held in Louvain-la-Neuve. Topics include: wave propogation; numerical modelling; identification of poromechanical parameters; and constitutive modelling.

The quality of concrete depends on numerous factors. One important factor is the physical property of mineral aggregates contained in the mix. Such mineral aggregates can be characterized by shape, roughness, and size of component particles. A limited number of methods are available to quantify mathematically or statistically the geometrical attributes of these usually irregular particles. One of these methods is derived from fractal geometry. The fractal dimension is not an integer like the topological or Euclidean dimension. The fractal dimension is capable of quantifying the geometrical irregularity of a solid object from a statistical point of view. The fractal analysis system for an aggregate shape has been successfully developed by integrating an image acquisition system with the three computer programs written specifically for this system. The results using the profile data with the known boundary fractal dimension demonstrated that the system developed in this study can be reliable for analysis of boundary fractal dimension thereby quantifying the irregularity of an object.

Bioengineering applies engineering methods, applied mathematics and physics to the study of biological problems, leading to a better understanding of systems such as the mechanics of physiological processes. Numerical analysis techniques are used to understand these processes by way of simulation. Both computational facilities and numerical techniques have given the medical community the ability to analyze, manage and visualize biomedical data. This volume contains the proceedings of the First International Conference on Simulation Modelling in Bioengineering, held in Merida, Venezuela in October 1996."

Fractals are intricate geometrical forms that contain miniature copies of themselves on ever smaller scales. This colorful book describes methods for producing an endless variety of fractal art using a computer program that searches through millions of equations looking for those few that can produce images having aesthetic appeal. Over a hundred examples of such images are included with a link to the software that produced these images, and can also produce many more similar fractals. The underlying mathematics of the process is also explained in detail.Other books by the author that could be of interest to the reader are Elegant Chaos: Algebraically Simple Chaotic Flows (J C Sprott, 2010) and Elegant Circuits: Simple Chaotic Oscillators (J C Sprott and W J Thio, 2020).