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Fractals Books

Fractals 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.

A tale of two fractals

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.

Author(s):

s 134Pages

Lectures on fractal geometry and dynamics

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.

Author(s):

s 96Pages

Lectures On Fractals And Dimension Theory

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.

Author(s):

s 106Pages

Fractals in the Plane the Ergodic Theory Methods

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.

Author(s):

s 324Pages

Conformal Dynamics

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.

Author(s):

s NAPages

Chaos, Fractals, and Arcadia

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.

Author(s):

s NAPages

Chaos and Fractals New Frontiers of Sciences

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Author(s):

s NAPages

The Fractal Geometry of the Mandelbrot Set, The Periods of the Bulbs

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Author(s):

s NAPages

The Fractal Geometry of the Mandelbrot Set, How to Count and How to Add

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Author(s):

s NAPages

Fractals A Fractals Lesson for Elementary and Middle School Students

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Author(s):

s NAPages

Lecture Notes on Fractal Geometry

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Author(s):

s NAPages