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

fractal representation.

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

of images.

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

fractals.

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

Consciousness

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).

Continue to: