Best Fractal Mathematics Books
Here you will get Best Fractal Mathematics Books For you.This is an up-to-date list of recommended books.
1. Chaos: Making a New Science
Author: by James Gleick
Published at: Penguin Books; Anniversary, Reprint edition (August 26, 2008)
The million-copy bestseller by National Book Award nominee and Pulitzer Prize finalist James Gleickthe author of Time Travel: A Historythat reveals the science behind chaos theoryA work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time.
From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science.
In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.
2. The Misbehavior of Markets: A Fractal View of Financial Turbulence
Author: by Benoit Mandelbrot
Published at: Basic Books; Annotated edition (March 7, 2006)
Benoit B.Mandelbrot, one of the century’s most influential mathematicians, is world-famous for making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth.
To these classic lines we can now add another example: Markets are not the safe bet your broker may claim. In his first book for a general audience, Mandelbrot, with co-author Richard L. Hudson, shows how the dominant way of thinking about the behavior of markets-a set of mathematical assumptions a century old and still learned by every MBA and financier in the world-simply does not work.
As he did for the physical world in his classic The Fractal Geometry of Nature , Mandelbrot here uses fractal geometry to propose a new, more accurate way of describing market behavior. The complex gyrations of IBM’s stock price and the dollar-euro exchange rate can now be reduced to straightforward formulae that yield a far better model of how risky they are.
3. Math Art: Truth, Beauty, and Equations
Author: by Stephen Ornes
Published at: Sterling; Illustrated edition (April 16, 2019)
From geometry in motion to the possibilities of pi, this stunning volume reveals how art has been inspired by the beauty and poetry of mathematical principles. The worlds of visual art and mathematics come together in this spectacular volume by award-winning writer Stephen Ornes.
He explores the growing sensation of math art, presenting more than 80 pieces, including a crocheted, colorful representation of non-Euclidian geometry that looks like sea coral and a 65-ton, 28-foot-tall bronze sculpture covered in a space-filling curve. For each work, we get the artist’s story followed by accessible and thought-provoking explanations of the mathematical concept and equations behind the art.
From 3D-printed objects that give real form to abstract mathematical theories, to mystic fractals, to Andy Warhol as a solution to the Traveling Salesman Problem, these artworks embody some of strangest, most beautiful relationships among numbers and across dimensions.
4. Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies
Author: by Geoffrey West
Published at: Penguin Books; Reprint edition (May 15, 2018)
“This is science writing as wonder and as inspiration.” The Wall Street Journal Wall Street JournalFrom one of the most influential scientists of our time, a dazzling exploration of the hidden laws that govern the life cycle of everything from plants and animals to the cities we live in.
Visionary physicist Geoffrey West is a pioneer in the field of complexity science, the science of emergent systems and networks. The term complexity can be misleading, however, because what makes West’s discoveries so beautiful is that he has found an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses.
Fascinated by aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science: West found that despite the riotous diversity in mammals, they are all, to a large degree, scaled versions of each other.
5. Patterns of the Universe: A Coloring Adventure in Math and Beauty
Author: by Alex Bellos
Published at: The Experiment; Illustrated edition (December 1, 2015)
An ingenious coloring book that reveals math’s hidden beautyand contemplative poweras never before Publisher’s note: Patterns of the Universe was previously published under the title Snowflake, Seashell, Star. Contemplate the Patterns of the Universe as you color! Math is at the heart of many natural wonders and has an abstract beauty all its ownin the silhouette of a snowflake, the spiral seeds of a sunflower, and the symmetry of the Sri Yantra mandala.
From the 4-D hypercube that casts a starlike shadow, to the infinite pattern of Penrose tiles that never perfectly repeats, these 57 exquisite designs reveal their secrets as you fill them with color. Art becomes an act of discoveryno math knowledge is required!
In the bonus Creating section, as you join dots, flip coins, and follow other simple steps, 12 surprising images will emerge before your eyes. This is an adventure for all agesand a treasure for artists in Numberland!
6. Antenna Theory: Analysis and Design
Author: by Constantine A. Balanis
Published at: Wiley; 4th edition (February 1, 2016)
Updated with color and gray scale illustrations, a companion website housing supplementary material, and new sections covering recent developments in antenna analysis and designThis book introduces the fundamental principles of antenna theory and explains how to apply them to the analysis, design, and measurements of antennas.
Due to the variety of methods of analysis and design, and the different antenna structures available, the applications covered in this book are made to some of the most basic and practical antenna configurations. Among these antenna configurations are linear dipoles; loops; arrays; broadband antennas; aperture antennas; horns; microstrip antennas; and reflector antennas.
The text contains sufficient mathematical detail to enable undergraduate and beginning graduate students in electrical engineering and physics to follow the flow of analysis and design. Readers should have a basic knowledge of undergraduate electromagnetic theory, including Maxwell’s equations and the wave equation, introductory physics, and differential and integral calculus.
7. On Growth and Form: The Complete Revised Edition
Author: by DArcy Wentworth Thompson
Published at: Dover Publications; Revised edition (June 23, 1992)
In this classic of biology and modern science, Sir D’Arcy Wentworth Thompson (18601948), one of the most distinguished scientists of the modern era, sets forth his seminal “theory of transformation” – that one species evolves into another not by successive minor changes in individual body parts but by large-scale transformations involving the body as a whole.
First written in 1917, the book was revised by Thompson in 1942 the revision reprinted here. The esteem in which this monumental, lavishly illustrated work is universally held derives not only from its scholarship and creativity, but also from the rich literary style that exemplifies Thompson’s great erudition in the physical and natural sciences, ancient and modern languages and the humanities.
The book begins with studies of organic magnitude, the rate of growth, cellular form and structure, adsorption, and the forms of tissues, then examines a vast spectrum of life forms, and concludes with a comparison of related forms that leads to the theory of transformations.
8. Fractals: Form, Chance and Dimension
Author: by Benoit B. Mandelbrot
Published at: Echo Point Books & Media; Reprint ed. edition (February 25, 2020)
Discover the Hidden Mathematics of Modern Geometry Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature.
Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot’s revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets.
Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.
9. The Fractal Geometry of Nature
Author: by Benoit B. Mandelbrot
Published at: Times Books; 2nd prt. edition (January 1, 1982)
Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature’s shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.
Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.
10. Mysterious Patterns: Finding Fractals in Nature
Author: by Sarah C. Campbell
Published at: Boyds Mills Press; Illustrated edition (April 1, 2014)
Nature’s repeating patterns, better known as fractals, are beautiful, universal, and explain much about how things grow. Fractals can also be quantified mathematically. Here is an elegant introduction to fractals through examples that can be seen in parks, rivers, and our very own backyards.
Readers will be fascinated to learn that broccoli florets are fractalsjust like mountain ranges, river systems, and treesand will share in the wonder of math as it is reflected in the world around us. Perfect for any elementary school classroom or library, Mysterious Patterns is an exciting interdisciplinary introduction to repeating patterns.
11. Visions of the Universe: A Coloring Journey Through Math’s Great Mysteries
Author: by Alex Bellos
Published at: The Experiment; Clr Csm edition (November 29, 2016)
Peek behind the scenes of the universeand see math in brilliant color! For curious minds throughout history, math was truly an art. In Visions of the Universe, you can pick up right where Isaac Newton, Blaise Pascal, and other luminaries left offby coloring 58 exquisite patterns inspired by great discoveries in math:Intricate geometric designs like those that grace the mosques of MeccaFelix Klein’s astounding diagramdrawn in 1897of light reflecting between five mirrored spheresA mind-bending puzzle so beautiful it once hung outside a Japanese temple, and more!
Plus, in the Creating chapter, you’ll help complete 10 additional images by following simple steps that give spectacular results. No math knowledge is required: Anyone can be an artist in Numberland!
12. Proof and the Art of Mathematics
Author: by Joel David Hamkins
Published at: The MIT Press (September 29, 2020)
An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs.
These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision.
13. In Focus Sacred Geometry: Your Personal Guide (In Focus, 12)
Author: by Bernice Cockram
Published at: Wellfleet (January 12, 2021)
With In Focus Sacred Geometry, learn the fascinating history behind this ancient tradition as well as how to decipher the geometrical symbols, formulas, and patterns based on mathematical patterns. People have searched for the meaning behind mathematical patterns for thousands of years.
At its core, sacred geometry seeks to find the universal patterns that are found and applied to the objects surrounding us, such as the designs found in temples, churches, mosques, monuments, art, architecture, and nature. Learn the fundamental principles behind:Interpreting the sacred symbolism and principles behind shapesCalculating numbers used in sacred geometryApplying the golden ratio and Fibonacci’s Sequence to objectsTranslating symbolic and geometrical letters and alphabets This accessible and beautifully designed guide to sacred geometry includes a frameable poster of the main sacred geometrical shapes and their unique, innate arrangements.
The In Focus series applies a modern approach to teaching the classic body, mind, and spirit subjects. Authored by experts in their respective fields, these beginner’s guides feature smartly designed visual material that clearly illustrates key topics within each subject.
14. Trading Chaos: Maximize Profits with Proven Technical Techniques
Author: by Justine Gregory-Williams
Published at: John Wiley & Sons, Publishers; 2nd edition (February 27, 2004)
How to trade the markets by integrating Chaos Theory with market sentiment In the first edition of Trading Chaos, seasoned trader and psychologist Bill Williams detailed the potential of Chaos Theory-which seeks to make the unpredictable understandable-in trading and it revolutionized financial decision-making.
The Second Edition of Trading Chaos is a cutting edge book that combines trading psychology and Chaos Theory and its particular effect on the markets. By examining both of these facets in relation to the current market, readers will have the best of all possible worlds when trading.
Bill Williams, PhD, CTA (Solana Beach, CA), is President of Profitunity. Com, a leader in the field of education for traders and investors. Justine Gregory-Williams (Solana Beach, CA) is President of the Profitunity Trading Group and a full-time trader.