Tag: Fractal

Fractional Calculus for Skeptics I The Fractal Paradigm


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English | 2024 | ISBN: 1032741554 | 147 Pages | PDF (True) | 21 MB
Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem.

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Fractal Antenna Design using Bio-inspired Computing Algorithms


Free Download Fractal Antenna Design using Bio-inspired Computing Algorithms by Balwinder S. Dhaliwal, Suman Pattnaik, Shyam Sundar Pattnaik
English | June 20, 2023 | ISBN: 9815136364 | 153 pages | MOBI | 2.15 Mb
This book presents research focused on the design of fractal antennas using bio-inspired computing techniques. The authors present designs for fractal antennas having desirable features like size reduction characteristics, enhanced gain, and improved bandwidths. The research is summarized in six chapters which highlight the important issues related to fractal antenna design and the mentioned computing techniques. Chapters demonstrate several applied concepts and techniques used in the process such as Artificial Neural Networks (ANNs), Genetic Algorithms (GAs), Particle Swarm Optimization (PSO) and Bacterial Foraging Optimization (BFO). The work aims to provide cost-effective and efficient solutions to the demand for compact antennas due to the increasing demand for reduced sizes of components in modern wireless communication devices.

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Ultra Fractal 6.06 Extended Edition


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Ultra Fractal 6 is a great way to create your own fractal art. Today, fractals are much more than the Mandelbrot sets that you may have seen before. With Ultra Fractal, you can choose from thousands of fractal types and coloring algorithms, zoom in as far as you want, use gradients to add color, and apply multiple layers to combine different fractals in one image. Ultra Fractal is very easy to use and yet more capable than any other fractal program. No mathematics required!

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Fractal Calculus and its Applications Fα-Calculus


Free Download Fractal Calculus and its Applications: Fα-Calculus by Alireza Khalili Golmankhaneh
English | August 29, 2022 | ISBN: 9811261105 | 311 pages | MOBI | 61 Mb
Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.

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The Science of Fractal Images


Free Download The Science of Fractal Images by Michael F. Barnsley , Robert L. Devaney , Benoit B. Mandelbrot , Heinz-Otto Peitgen , Dietmar Saupe , Richard F. Voss
English | PDF | 1988 | 328 Pages | ISBN : 1461283493 | 37.4 MB
This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH ’87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot’s fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.

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Fractal Patterns with MATLAB


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English | 2023 | ISBN: 3031481011 | 96 Pages | PDF EPUB (True) | 29 MB
This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces.

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Fractal Architecture Organic Design Philosophy in Theory and Practice


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English | 2012 | pages: 424 | ISBN: 0826352014 | PDF | 211,7 mb
Throughout history, nature has served as an inspiration for architecture and designers have tried to incorporate the harmonies and patterns of nature into architectural form. Alberti, Charles Renee Macintosh, Frank Lloyd Wright, and Le Courbusier are just a few of the well- known figures who have taken this approach and written on this theme. With the development of fractal geometry-the study of intricate and interesting self- similar mathematical patterns-in the last part of the twentieth century, the quest to replicate nature’s creative code took a stunning new turn. Using computers, it is now possible to model and create the organic, self-similar forms of nature in a way never previously realized.

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The Fractal Organization Creating Enterprises of Tomorrow


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English | ISBN: 9351502449 | 2015 | 360 pages | EPUB | 2 MB
The biggest challenge facing leaders today is the creation of organizations that are capable of surviving and flourishing in these uncertain times. How does one create an organization that is sustainable in the long run, how can organizations be ready for uncertainties that the markets place upon them, how can an organization be simply brilliant by design? This book leverages the proposed meta-theory for progressive organizational design and dynamics real-world reflections to create fractal-based sustainable enterprises of tomorrow.

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