This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
Some references are:
M. Barnsley, "Fractals Everywhere", Academic Press Inc., 1988, 1993.
ISBN 0-12-079062-9. This is an excellent text book on fractals. This
is probably the best book for learning about the math underpinning
fractals. It is also a good source for new fractal types.
M. Barnsley, "The Desktop Fractal Design System" Versions 1 and 2.
1992, 1988. Academic Press. Available from Iterated Systems.
M. Barnsley and P H Lyman, "Fractal Image Compression". 1993. AK
Peters Limited. Available from Iterated Systems.
M. Barnsley and L. Anson, "The Fractal Transform", Jones and Bartlett,
April, 1993. ISBN 0-86720-218-1. This book is a sequel to "Fractals
Everywhere". Without assuming a great deal of technical knowledge, the
authors explain the workings of the Fractal Transform(tm). The Fractal
Transform is the compression tool for storing high-quality images in a
minimal amount of space on a computer. Barnsley uses examples and
algorithms to explain how to transform a stored pixel image into its
R. Devaney and L. Keen, eds., "Chaos and Fractals: The Mathematics
Behind the Computer Graphics", American Mathematical Society,
Providence, RI, 1989. This book contains detailed mathematical
descriptions of chaos, the Mandelbrot set, etc.
R. L. Devaney, "An Introduction to Chaotic Dynamical Systems",
Addison- Wesley, 1989. ISBN 0-201-13046-7. This book introduces many
of the basic concepts of modern dynamical systems theory and leads the
reader to the point of current research in several areas. It goes into
great detail on the exact structure of the logistic equation and other
1-D maps. The book is fairly mathematical using calculus and topology.
R. L. Devaney, "Chaos, Fractals, and Dynamics", Addison-Wesley, 1990.
ISBN 0-201-23288-X. This is a very readable book. It introduces chaos
fractals and dynamics using a combination of hands-on computer
experimentation and precalculus math. Numerous full-color and black
and white images convey the beauty of these mathematical ideas.
R. Devaney, "A First Course in Chaotic Dynamical Systems, Theory and
Experiment", Addison Wesley, 1992. A nice undergraduate introduction
to chaos and fractals.
A. K. Dewdney, (1989, February). Mathematical Recreations. "Scientific
American", pp. 108-111.
G. A. Edgar, "Measure Topology and Fractal Geometry", Springer-Verlag
Inc., 1990. ISBN 0-387-97272-2. This book provides the math necessary
for the study of fractal geometry. It includes the background material
on metric topology and measure theory and also covers topological and
fractal dimension, including the Hausdorff dimension.
K. Falconer, "Fractal Geometry: Mathematical Foundations and
Applications", Wiley, New York, 1990.
J. Feder, "Fractals", Plenum Press, New York, 1988. This book is
recommended as an introduction. It introduces fractals from
geometrical ideas, covers a wide variety of topics, and covers things
such as time series and R/S analysis that aren't usually considered.
Y. Fisher (ed), "Fractal Image Compression: Theory and Application".
Springer Verlag, 1995.
L. Gardini (ed), "Chaotic Dynamics in Two-Dimensional Noninvertive
Maps". World Scientific 1996, ISBN: 9810216475
J. Gleick, "Chaos: Making a New Science", Penguin, New York, 1987.
B. Hao, ed., "Chaos", World Scientific, Singapore, 1984. This is an
excellent collection of papers on chaos containing some of the most
significant reports on chaos such as "Deterministic Nonperiodic Flow"
by E.N. Lorenz.
I. Hargittai and C. Pickover. "Spiral Symmetry" 1992 World Scientific
Publishing, River Edge, New Jersey 07661. ISBN 981-02-0615-1. Topics:
Spirals in nature, art, and mathematics. Fractal spirals, plant
spirals, artist's spirals, the spiral in myth and literature... Loads
H. Jürgens, H. O Peitgen, & D. Saupe. 1990 August, The Language of
Fractals. "Scientific American", pp. 60-67.
H. Jürgens, H. O. Peitgen, H.O., & D. Saupe, 1992, "Chaos and
Fractals: New Frontiers of Science". New York: Springer-Verlag.
S. Levy, "Artificial life : the quest for a new creation", Pantheon
Books, New York, 1992. This book takes off where Gleick left off. It
looks at many of the same people and what they are doing post-Gleick.
B. Mandelbrot, "The Fractal Geometry of Nature", W. H. FreeMan, New
York. ISBN 0-7167-1186-9. In this book Mandelbrot attempts to show
that reality is fractal-like. He also has pictures of many different
B. Mandelbrot, "Les objets fractals", Flammarion, Paris. ISBN
2-08-211188-1. The French Mandelbrot's book, where the word "fractal"
has been used for the first time.
J.L. McCauley, "Chaos, dynamics, and fractals : an algorithmic
approach to deterministic chaos", Cambridge University Press, 1993.
E. R. MacCormac (ed), M. Stamenov (ed), "Fractals of Brain, Fractals
of Mind : In Search of a Symmetry Bond (Advances in Consciousness
Research, No 7)", John Benjamins, ISBN: 1556191871, Subjects include:
Neural networks (Neurobiology), Mathematical models, Fractals, and
G.V. Middleton, (ed), "1991: Nonlinear Dynamics, Chaos and Fractals
(w/ application to geological systems)" Geol. Assoc. Canada, Short
Course Notes Vol. 9, 235 p. This volume contains a disk with some
examples (also as pascal source code) ($25 CDN)
T.F. Nonnenmacher, G.A Losa, E.R Weibel (ed.) "Fractals in Biology and
Medicine" ISBN 0817629890, Springer Verlag, 1994
L. Nottale, "Fractal Space-Time and Microphysics, Towards a Theory of
Scale Relativity", World Scientific (1993).