Fractal Geometry Books

Bassingthwaighte, James B., Larry S. Liebovitch, and Bruce J. West. Fractal Physiology. New York : Oxford University Press, 1994.

Notes: Part III, Physiological applications of fractal geometry: ion channels, heart muscle, neurons, vascular flows, growth.

Crilly, A. J., R. A. Earnshaw, and H. Jones, eds. Fractals and Chaos. New York: Springer-Verlag, 1991.

Notes: Part 1: 7 chapters on fractal geometry including applications to growth, image synthesis, and neural nets.

Part 2: 6 chapters on chaos theory, including applications to physical systems.

Dubrulle, B., F. Graner, and D. Sornette. Scale Invariance and Beyond. New York: Springer-Verlag, 1997.

Notes: Applications of fractals and wavelets to: condensed matter, cosmology, earthquakes, biology, finance, turbulence, DNA sequences, gravity, metallurgy.

Devaney, Robert L., and Linda Keen, eds. Chaos and Fractals: The Mathematics Behind the Computer Graphics.

Providence, RI: Amer. Math. Soc, 1989.

Notes: Lecture notes from an AMS short course from 1988, by Devaney, Holmes, Alligood and Yorke, Keen,

Branner, Harrison, and Barnsley.

Edgar, Gerald A., ed. Classics on Fractals. Reading, MA: Addison-Wesley, 1993.

Notes: Papers by Weierstrass, Cantor, Hausdorff and others, in chronological order, 1872-1967.

Evertsz, C.J.G., H.-O. Peitgen, R.F. Voss, eds. Fractal Geometry and Analysis: the Mandelbrot Festschrift, Curacao 1995.

Singapore; River Edge, NJ: World Scientific, 1996.

Notes: Conference proceedings.

Falconer, K. J. The Geometry of Fractal Sets.

Cambridge, New York : Cambridge University Press, 1985.

Notes: Great text on fractal dimensions.

Falconer, K. J. Fractal Geometry : Mathematical Foundations and Applications.

Chichester ; New York : Wiley, c1990.

Notes: Basic text including multifractals. Applications include: chaotic attractors of dynamical systems, percolation, brownian motion, turbulence, growth, e-m and gravitational potentials.

Falconer, K. J. Techniques in fractal geometry. Chichester ; New York Wiley, c1997.

Feder, Jens. Fractals. New York: Plenum Press, 1988.

Notes: Excellent text, esp. for the application of fractal geometry to porous media and percolation (ie, oil).

Harte, David. Multifractals : Theory and Applications.

Boca Raton : Chapman & Hall/CRC c2001.

Notes: Applications include:

• invariant measures on chaotic attractors,
• energy dissapation in turbulent fluid flows,
• rainfall fields, and
• earthquake locations.

and others are mentionned: financial data and internet traffic.

Hastings, Harold M., and George Sugihara. Fractals : A User's Guide for the Natural Sciences.

Oxford ; New York : Oxford University Press, 1993.

Notes: Applications include: earthquake models, pancreatic islets, neuronal processes, temperature and rainfall data.

Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York, NY: W. H. Freeman, 1975.

Notes: This is it: the classic of classics by the master. Lots of applications: coastlines, galaxies, percolation, brownian motion, economics.

Mandelbrot, Benoit B. Multifractals and 1/f Noise: Wild Self-Affinity in Physics (1963-1976).

New York, NY: Springer-Verlag, 1999.

Notes: Collection of papers by Mandelbrot and others.

Massopust, Peter R. Fractal Functions, Fractal Surfaces, and Wavelets.

New York, NY: Academic Press, 1994.

Notes: Ch. 4 (Fractal dimension of chaotic attractors) and Ch. 7 (Fractals and wavelets) are interesting.

Peitgen, Heinz-Otto, J.M. Henriques, and L.F. Penedo, eds.

Fractals in the Fundamental and Applied Sciences :

Proceedings of the First IFIP Conference on Fractals

in the Fundamental and Applied Sciences.

Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A., 1991.

Notes: Conference proceedings. Apploications include: turbulence, electron transport, musical composition,

microbial growth, earthquke faults, brownian motion.

Peitgen, Heinz-Otto, Hartmut Jurgens, and Dietmar Saupe.

Fractals for the Classroom. Part One: Introduction to Fractals and Chaos.

New York, NY: Springer-Verlag, 1992.

Notes: Fractals and chaos go to high school! Introductory material on fractal geometry,

including applications to image synthesis, evolved from a lecture by Peitgen to the NCTM in 1988.

Peitgen, Heinz-Otto, Hartmut Jurgens, and Dietmar Saupe.

Fractals for the Classroom. Part Two: xxxx.

New York, NY: Springer-Verlag, 1992.

Notes: Introductory material on chaos theory, including applications to growth.

Peitgen, Heinz-Otto, Hartmut Jurgens, and Dietmar Saupe. Chaos and Fractals : New Frontiers of Science.

New York: Springer-Verlag, c1992.

Peitgen, Heinz-Otto, and Dietmar Saupe, eds. The Science of Fractal Images.

New York: Springer-Verlag, c1988.

Peitgen, Heinz-Otto, and P.H. Richter. The Beauty of Fractals: Images of Complex Dynamical Systems.

Berlin; New York: Springer-Verlag, c1986.

Scholz, Christopher H. and Benoit B. Mandelbrot. Fractals and Geophysics.

Basel ; Boston : Birkhauser Verlag, 1989.

UCB Earth Sci QC801 .G37 v.131:1-2

Schroeder, M. R. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise.

New York: W.H. Freeman, c1991.

Notes: Lots of theory and applications here: image synthesis, hydrodynamics, psychology, acoustics, music, epidemics, physics, tomography, gambling, astronomy, percolation.

Triebel, Hans. Fractals and Spectra Related to Fourier Analysis and Function Spaces.

Basel: Birkhauser-Verlag, 1997.

Notes: Rigorous math, function spaces of fractals.

West, Bruce J. Fractal Physiology and Chaos in Medicine. Singapore ; Teaneck, N.J. : World Scientific, c1990.

Notes: This is primarily about chaotic dynamics in physiology: epidemics, neurons, chemistry, cardiology, and epilepsy.