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Free Fractals Books

Abstract Algebra
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Linear Algebra
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Commutative Algebra
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Complex Algebra
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Elliptic Curves
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Geometric Algebra
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Groups Theory
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Higher Algebra
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Homological Algebra
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Lie Algebra
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Differential Algebra
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Rings and Fileds
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Geometry
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Algebraic Geometry
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Differential Geometry
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Fractals
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Riemannian Geometry
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Mathematical Analysis
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Complex Analysis
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Functional Analysis
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Differential Analysis
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Fourier Analysis
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Harmonic Analysis
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Numerical Analysis
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Real Analysis
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Topology
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Algebraic Topology
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Differential Topology
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Geometric Topology
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K-theory
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Applied Mathematics
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Calculus
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Differential Equations
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Combinatorics
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Discrete Mathematics
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Graph Theory
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Number Theory
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Probability Theory
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Set Theory
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Trigonometry
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Category Theory
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Constants & Numerical Sequences
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Basic Mathematics
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Classical Analysis
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History of Mathematics
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Arithmetic Geometry
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Mathematical Series
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Modern Geometry
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Basic Algebra
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Differential Equations
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Online Books

This section contains free e-books and guides on Fractals, some of the resources in this section can be viewed online and some of them can be downloaded.

Fractals Books
Online Books
A tale of two fractals

PDF | 134 Pages | English
This book is devoted to a phenomenon of fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach.

 
Lectures on fractal geometry and dynamics

PDF | 96 Pages | English
Goal of this course note is primarily to develop the foundations of geometric measure theory, and covers in detail a variety of classical subjects. A secondary goal is to demonstrate some applications and interactions with dynamics and metric number theory.

 
Lecture Notes On Dynamical Systems, chaos and Fractal Geometry

PDF | 258 Pages | English
The first 12 chapters cover fairly standard topics in one dimensional dynamics and should be accessible to most upper level undergraduate students. The requirements from real analysis and topology are developed as the material progresses. Chapter 13 gives an introduction to the theory of substitutions and shows how these can give rise to certain types of fractals. Subsequent chapters develop the rigorous mathematical theory of substitutions and Sturmian sequences.

 
Lectures On Fractals And Dimension Theory

PDF | 106 Pages | English
This note covers the following topics: Basic Properties and Examples, Iterated Function Schemes, Computing dimension, Some Number Theory and algorithms, Measures and Dimension, Classic results: Projections, Slices and translations, Tranversality and Iterated function schemes with overlaps.

 
Fractals in the Plane the Ergodic Theory Methods

PDF | 324 Pages | English
This book is an introduction to the theory of iteration of expanding and nonuniformly expanding holomorphic maps and topics in geometric measure theory of the underlying invariant fractal sets. Major topics covered: Basic examples and definitions, Measure preserving endomorphisms, Ergodic theory on compact metric spaces, Distance expanding maps, Thermodynamical formalism, Expanding repellers in manifolds and Riemann sphere, preliminaries, Cantor repellers in the line, Sullivanís scaling function, application in Feigenbaum universality, Fractal dimensions, Sullivanís classification of conformal expanding repellers, Conformal maps with invariant probability measures of positive, Lyapunov exponent and Conformal measures.

 
Conformal Dynamics

Online | NA Pages | English
This note covers the following topics: Rigidity and inflexibility in conformal dynamics, Hausdorff dimension and conformal dynamics: Strong convergence of Kleinian groups, Geometrically finite rational maps and Computation of dimension.

 
Chaos, Fractals, and Arcadia

Online | NA Pages | English
This note covers the following topics: Thomasina's Geometry of Irregular Forms, The Chaos Game, The Sierpinski Hexagon, Thomasina's Fern and Valentine's Grouse.

 
Chaos and Fractals New Frontiers of Sciences
The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs
The Fractal Geometry of the Mandelbrot Set, How to Count and How to Add
Fractals A Fractals Lesson for Elementary and Middle School Students
Lecture Notes on Fractal Geometry
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