Chapter 11
Thermodynamics and
fractals
11.1
The thermodynamic formalism
Here our goal is to establish equation (3.52) and to derive an equivalent expression that ts into the structure of statistical m
Chapter 2
Iterated function systems:
fractals as limits
Often a rst exposure to fractals consists of googling fractal geometry, nding
a program to generate fractals, selecting some example from a pres
Chapter 13
Valediction
I began teaching (some of) this material in 1988 at Union College. The following
year, David Peak and I started teaching fractals and chaos at a less mathematically sophisticate
Chapter 12
A brief survey of some
applications of fractal
geometry
A testament to how well fractal geometry ts nature and culture Benoit expressed this as, The world needs fractals, one of his mantras
Chapter 8
Nonlinear Fractals 3: Limit
Sets of Circle Inversions
and Kleinian Groups
Analogous to the fractals generated by IFS are the limit sets of circle inversions.
Circle inversion is an ancient g
Chapter 7
Nonlinear Fractals 2: The
Mandelbrot Set
The August, 1985, cover of Scientic American presented one of the rst widelydisseminated pictures of the Mandelbrot set. The accompanying article in
Chapter 6
Nonlinear Fractals 1: Julia
Sets and chaos
Nonlinearity makes the pictures generally more attractive than those of linear
fractals. A rich variety of nonlinear fractality is exhibited by Jul
Chapter 10
Cellular Automata and
Fractal Evolution
10.1
Self-reproducing machines
The idea of creating life from inanimate matter has attracted many imaginative
minds. The best-known exploration of th
Chapter 5
Quantifying Fractals 2:
Multifractals
Early methods of generating images of fractals involved a binary decomposition
of the plane, naturally following from that of Euclidean geometry. To dra
Chapter 9
Random Fractals
The most familiar fractals are deterministic: the Mandelbrot set and Julia sets,
Sierpinski gaskets, Koch curves, Cantor sets, IFS attractors, and the like. However, as a eld
Chapter 4
IFS revisited: memory
eects and data-driven
Inversion of an idea has a long, wonderful history in science, literature, and art.
Take a successful approach, step outside the familiar box it t