Download or read book Make Your Own Mandelbrot written by Tariq Rashid and published by CreateSpace. This book was released on 2014-04-02 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle journey through the mathematics of the Mandelbrot and Julia fractals, and making your own using the Python computer language. Mathematics can be fun, exciting, surprising, and stunningly beautiful. But too few people ever experience this, associating it instead with boring and apparently pointless exercises in trigonometry and solving equations. This guide will take you on an emotional journey, starting from very simple ideas, and exploring some surprising and intricately beautiful behaviors of the very simple mathematics that underlies the famous Mandelbrot fractal. You won't need anything more than basic school mathematics. Part 1 is about ideas. It introduces the mathematical ideas underlying the Mandelbrot fractal, gently with lots of illustrations and examples. Part 2 is practical. It introduces the popular and easy to learn Python programming language, and gradually builds up a program to calculate and visualise the Mandelbrot fractal. Part 3 extends these ideas. It reveals the related Julia fractals, creates 3-dimensional landscapes and shows how even more interesting images can be made using mathematical filters. The fractal image on the cover of this book is created using only the ideas and code developed in this book.
Download or read book Fractals and Chaos written by Benoit Mandelbrot and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.
Download or read book The Fractalist written by Benoit Mandelbrot and published by Vintage. This book was released on 2014-01-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the remarkable life story of Benoit Mandelbrot, the creator of fractal geometry, and his unparalleled contributions to science mathematics, the financial world, and the arts. Mandelbrot recounts his early years in Warsaw and in Paris, where he was mentored by an eminent mathematician uncle, through his days evading the Nazis in occupied France, to his education at Caltech, Princeton, and MIT, and his illustrious career at the IBM Thomas J. Watson Research Center. An outside to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden scientific laws. In the process he was able to use geometry to solve fresh, real-world problems. With exuberance and an eloquent fluency, Benoit Mandelbrot recounts the high points of his fascinating life, offering us a glimpse into the evolution of his extraordinary mind. With full-color inserts and black-and-white photographs throughout.
Download or read book Finding Our Way Home written by Myke Johnson and published by Lulu.com. This book was released on 2016-11-25 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this time of ecological crisis, all that is holy calls us into a more intimate partnership with the diverse and beautiful beings of this earth. In Finding Our Way Home, Myke Johnson reflects on her personal journey into such a partnership and offers a guide for others to begin this path. Lyrically expressed, it weaves together lessons from a chamomile flower, a small bird, a copper beech tree, a garden slug, and a forest fern, along with insights from Indigenous philosophy, environmental science, fractal geometry, childhood Catholic mysticism, the prophet Elijah, fairy tales, and permaculture design. This eco-spiritual journey also wrestles with the history of our society's destruction of the natural world, and its roots in the original theft of the land from Indigenous peoples. Exploring the spiritual dimensions of our brokenness, it offers tools to create healing. Finding Our Way Home is a ceremony to remember our essential unity with all of life.
Download or read book Chaos and Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
Download or read book Fractal Analysis Basic Concepts And Applications written by Carlo Cattani and published by World Scientific. This book was released on 2022-02-24 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a basic and self-contained introduction to the ideas underpinning fractal analysis. The book illustrates some important applications issued from real data sets, real physical and natural phenomena as well as real applications in different fields, and consequently, presents to the readers the opportunity to implement fractal analysis in their specialties according to the step-by-step guide found in the book.Besides advanced undergraduate students, graduate students and senior researchers, this book may also serve scientists and research workers from industrial settings, where fractals and multifractals are required for modeling real-world phenomena and data, such as finance, medicine, engineering, transport, images, signals, among others.For the theorists, rigorous mathematical developments are established with necessary prerequisites that make the book self-containing. For the practitioner often interested in model building and analysis, we provide the cornerstone ideas.
Download or read book The Mis Behaviour of Markets written by Benoit B. Mandelbrot and published by Profile Books. This book was released on 2010-10-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they have a shifting sense of time and wild behaviour that makes them volatile, dangerous - and beautiful. In his models, the complex gyrations of the FTSE 100 and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved.
Download or read book Geometry for the Artist written by Catherine A. Gorini and published by CRC Press. This book was released on 2023-05-26 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry for the Artist is based on a course of the same name which started in the 1980s at Maharishi International University. It is aimed both at artists willing to dive deeper into geometry and at mathematicians open to learning about applications of mathematics in art. The book includes topics such as perspective, symmetry, topology, fractals, curves, surfaces, and more. A key part of the book’s approach is the analysis of art from a geometric point of view—looking at examples of how artists use each new topic. In addition, exercises encourage students to experiment in their own work with the new ideas presented in each chapter. This book is an exceptional resource for students in a general-education mathematics course or teacher-education geometry course, and since many assignments involve writing about art, this text is ideal for a writing-intensive course. Moreover, this book will be enjoyed by anyone with an interest in connections between mathematics and art. Features Abundant examples of artwork displayed in full color Suitable as a textbook for a general-education mathematics course or teacher-education geometry course Designed to be enjoyed by both artists and mathematicians
Download or read book Dynamical Systems with Applications Using Mathematica written by Stephen Lynch and published by Birkhäuser. This book was released on 2017-10-12 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
Download or read book Computability of Julia Sets written by Mark Braverman and published by Springer Science & Business Media. This book was released on 2009-02-08 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
Download or read book Dynamical Systems with Applications using Python written by Stephen Lynch and published by Springer. This book was released on 2018-10-09 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.
Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot and published by Echo Point Books & Media, LLC. This book was released on 2021-07-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.
Download or read book Dorie s Cookies written by Dorie Greenspan and published by HarperCollins. This book was released on 2016-10-25 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: James Beard Award-winner for Best Baking and Dessert Book 2017 All-new collection from a "revered icon" and "culinary guru" (New York Times). Over the course of her baking career, Dorie Greenspan has created more than 300 cookie recipes. Yet she has never written a book about them—until now. To merit her “three purple stars of approval,” every cookie had to be so special that it begged to be made again and again. Cookies for every taste and occasion are here. There are company treats like Portofignos, with chocolate dough and port-soaked figs, and lunch-box Blueberry Buttermilk Pie Bars. They Might Be Breakfast Cookies are packed with goodies—raisins, dried apples, dried cranberries, and oats— while Almond Crackle Cookies have just three ingredients. There are dozens of choices for the Christmas cookie swaps, including Little Rascals (German jam sandwich cookies with walnuts), Italian Saucissons (chocolate log cookies studded with dried fruit), and Snowy-Topped Brownie Drops. And who but America’s favorite baker could devise a cookie as intriguing as Pink-Peppercorn Thumbprints or as popular as the World Peace Cookie, with its 59 million Internet fans?
Download or read book Fractals written by Jens Feder and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.
Download or read book Brainfilling Curves A Fractal Bestiary written by Jeffrey Ventrella and published by Lulu.com. This book was released on 2012-03-01 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: * A lovingly-crafted visual expedition, lead by a lifelong fractal wizard with an obsession for categorizing fractal species * Hundreds of beautiful color images * An in-depth taxonomy of Koch-constructed Fractal Curves * An intuitive introduction to Koch construction * A must-read for anyone interested in fractal geometry
Download or read book Math Adventures with Python written by Peter Farrell and published by No Starch Press. This book was released on 2019-01-08 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn math by getting creative with code! Use the Python programming language to transform learning high school-level math topics like algebra, geometry, trigonometry, and calculus! Math Adventures with Python will show you how to harness the power of programming to keep math relevant and fun. With the aid of the Python programming language, you'll learn how to visualize solutions to a range of math problems as you use code to explore key mathematical concepts like algebra, trigonometry, matrices, and cellular automata. Once you've learned the programming basics like loops and variables, you'll write your own programs to solve equations quickly, make cool things like an interactive rainbow grid, and automate tedious tasks like factoring numbers and finding square roots. You'll learn how to write functions to draw and manipulate shapes, create oscillating sine waves, and solve equations graphically. You'll also learn how to: - Draw and transform 2D and 3D graphics with matrices - Make colorful designs like the Mandelbrot and Julia sets with complex numbers - Use recursion to create fractals like the Koch snowflake and the Sierpinski triangle - Generate virtual sheep that graze on grass and multiply autonomously - Crack secret codes using genetic algorithms As you work through the book's numerous examples and increasingly challenging exercises, you'll code your own solutions, create beautiful visualizations, and see just how much more fun math can be!
Download or read book The Pollan Family Table written by Corky Pollan and published by Simon and Schuster. This book was released on 2016-06-07 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In The Pollan Family Table, Corky, Lori, Dana, and Tracy Pollan invite you into their warm, inspiring kitchens, sharing more than 100 of their family's best recipes. For generations, the Pollans have used fresh, local ingredients to cook healthy, irresistible meals. Michael Pollan, whose bestselling books have changed our culture and the way we think about food, writes in his foreword about how the family meals he ate growing up shaped his worldview. This stunning and practical cookbook gives you the tools you need to implement the Pollan food philosophy in your everyday life and to make great, nourishing, delectable meals that bring your family back to the table"--Jacket.
