The Family Tree Of Fractal Curves
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The Family Tree Of Fractal Curves
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Author : Jeffrey Ventrella
language : en
Publisher: Eyebrain Books
Release Date : 2019-07
The Family Tree Of Fractal Curves written by Jeffrey Ventrella and has been published by Eyebrain Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07 with Computers categories.
This book explains a taxonomy of plane-filling curves (fractal curves with a fractal dimension of 2). it includes the classic fractal curves described in Mandelbrot's original book. Many new fractal curves are introduced. The taxonomy is based upon the Gaussian integers and the Eisenstein integers - each forming a lattice (square and triangular). These lattices have algebraic properties, which allows number theory to be used in describing and classifying these curves. This work has been under development for over 30 years. An earlier version of this taxonomy is described in the book ""Brain-filling Curves"", also by Jeffrey Ventrella. More on plane-filling curves can be found at fractalcurves.com
Brainfilling Curves A Fractal Bestiary
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Author : Jeffrey Ventrella
language : en
Publisher: Lulu.com
Release Date : 2012-03-01
Brainfilling Curves A Fractal Bestiary written by Jeffrey Ventrella and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-01 with Computers categories.
* 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
Curves And Fractal Dimension
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Author : Claude Tricot
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-11-18
Curves And Fractal Dimension written by Claude Tricot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-18 with Mathematics categories.
Written for mathematicians, engineers, and researchers in experimental science, as well as anyone interested in fractals, this book explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length. The approach is by way of precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus while also containing material appropriate for graduate coursework in curve analysis and/or fractal dimension.
The Beauty Of Fractals
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Author : Denny Gulick
language : en
Publisher: MAA
Release Date : 2010
The Beauty Of Fractals written by Denny Gulick and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.
Fractal Curves
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Author : Source Wikipedia
language : en
Publisher: University-Press.org
Release Date : 2013-09
Fractal Curves written by Source Wikipedia and has been published by University-Press.org this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 33. Chapters: Blancmange curve, De Rham curve, Dragon curve, Gosper curve, Hilbert curve, Koch snowflake, Levy C curve, List of fractals by Hausdorff dimension, Minkowski's question mark function, Moore curve, N-flake, Sierpi ski arrowhead curve, Sierpi ski curve, Singular function, Space-filling curve, Weierstrass function, Z-order curve. Excerpt: According to Falconer, one of the essential features of a fractal is that its Hausdorff dimension strictly exceeds its topological dimension. Presented here is a list of fractals ordered by increasing Hausdorff dimension, with the purpose of visualizing what it means for a fractal to have a low or a high dimension. In mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass. Historically, the Weierstrass function is important because it was the first published example (1872) to challenge the notion that every continuous function was differentiable except on a set of isolated points. In Weierstrass' original paper, the function was defined by where, is a positive odd integer, and This construction, along with the proof that it is nowhere differentiable, was first given by Weierstrass in a paper presented to the Konigliche Akademie der Wissenschaften on 18 July 1872. The proof that this function is continuous everywhere is not difficult. Since the terms of the infinite series which defines it are bounded by a and this has finite sum for 0
Fractal Curves And Complexity
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Author : James E. Cutting
language : en
Publisher:
Release Date : 1987
Fractal Curves And Complexity written by James E. Cutting and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Fractals A Very Short Introduction
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Author : Kenneth Falconer
language : en
Publisher: OUP Oxford
Release Date : 2013-09-26
Fractals A Very Short Introduction written by Kenneth Falconer and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Mathematics categories.
Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
The Geometry Of Fractal Sets
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Author : K. J. Falconer
language : en
Publisher: Cambridge University Press
Release Date : 1985
The Geometry Of Fractal Sets written by K. J. Falconer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Fractals In Probability And Analysis
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Author : Christopher J. Bishop
language : en
Publisher: Cambridge University Press
Release Date : 2017
Fractals In Probability And Analysis written by Christopher J. Bishop and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Parametrizations Of Fractal Curves
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Author : Annina Iseli
language : en
Publisher:
Release Date : 2014
Parametrizations Of Fractal Curves written by Annina Iseli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.