• Title: Fractals in Probability and Analysis
• Author(s) Christopher J. Bishop, Yuval Peres
• Publisher: Cambridge University Press (January 30, 2017); eBook (Preprint)
• Paperback: 412 pages
• eBook: PDF
• Language: English
• ASIN/ISBN-10: 1107134110
• ISBN-13: 978-1107134119
• Share This:  

Book Description

This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem.

• Christopher J. Bishop is a professor in the Department of Mathematics at Stony Brook University, New York.

• Amazon

• Fractal Geometry and Fractals
• Calculus and Mathematical Analysis
• Probability Theory and Stochastic Processes
• Geometry and Topology

• Fractals in Probability and Analysis (Christopher J. Bishop, et al.)
• The Mirror Site (1) - PDF
• The Mirror Site (2) - PDF

• Fractals: Art to Applied Science (Benjamin Kenwright)

  This text is a reference for learning and mastering Fractals (theoretical and applied perspective). It discuss how the fractal algorithms function, present code examples in editable sandboxes with explanations.

• Fractal Geometry: Mathematical Foundations and Applications

  This book has become a seminal text on the mathematics of Fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines.

• A Tale of Two Fractals (A.A. Kirillov)

  This book provides an original treatment of Fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. It is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals.

• Fractal Geometry (Mark McClure, et al.)

  Fractal geometry is a new way of looking at the world. This book combines text and graphics to offer the most accessible amount that any reader is likely to find, helping in the overall move toward scientific literacy.

• Strange Attractors: Creating Patterns in Chaos (Julien C. Sprott)

  This book describes a simple method for generating an endless succession of beautiful Fractal patterns by iterating simple maps and ordinary differential equations with coefficients chosen automatically by the computer.

• Conformal Fractals: Ergodic Theory Methods (Feliks Przytycki, ...)

  This is a one-stop introduction to the methods of Ergodic Theory applied to holomorphic iteration. Focus on the field of 1-dimensional holomorphic iterations and underlying Fractal sets, from the point of view of geometric measure theory and rigidity.

• Random Fractals (Peter Morters)

  Random Fractals are the method of choice when it comes to modelling landscapes, clouds and other natural phenomena. Describes the fundamentals of random fractals and some of the basic methods for their generation.

• The Fractal Geometry of Nature (Benoit Mandelbrot)

  Explore the wondrously complex repeating shapes of the natural world in The Fractal Geometry of Nature. Written in a style that is accessible to a wide audience, computer scientist, professor, mathematician, etc.