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 mechanics. The application of
thermodynamic methods to f
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 preset menu, and
clicking the RUN button. The image drifts
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 sophisticated level, an introduction to scientic thinking for non-s
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 is the observation that many applications of fractals
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 geometric construction suggested by reection in
a circul
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 the
Computer Recreations column contained several more
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 Julia sets. Powerful tools for studying complex analytic f
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 this topic is certainly Mary Shelleys 1818
novel Frankens
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 draw a
lled-in square, paint black the square and the regi
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 fractals were born in the study of random processes, i
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 ts, turn it on its
head, see how it looks from a dierent