This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
"Chaos: Making a New Science", by James Gleick, is a good book
to get a general overview and history that does not require an
extensive math background. "Fractals Everywhere," by Michael Barnsley,
and "Measure Topology and Fractal Geometry", by G. A. Edgar, are
textbooks that describe mathematically what fractals are and how to
generate them, but they requires a college level mathematics
background. "Chaos, Fractals, and Dynamics", by R. L. Devaney, is also
a good start. There is a longer book list at the end of the FAQ (see
"What are some general references?").
Also, there are networked resources available, such as :
Exploring Fractals and Chaos
http://www.lib.rmit.edu.au/fractals/exploring.html
Fractal Microscope
http://www.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html
Dynamical Systems and Technology Project: a introduction for
high-school students
http://math.bu.edu/DYSYS/dysys.html
An Introduction to Fractals (Written by Paul Bourke)
http://www.mhri.edu.au/~pdb/fractals/fracintro/
Fractals and Scale (by David G. Green)
http://life.csu.edu.au/complex/tutorials/tutorial3.html
What are fractals? (by Neal Kettler)
http://www.vis.colostate.edu/~user1209/fractals/fracinfo.html
Fract-ED a fractal tutorial for beginners, targeted for high
school/tech school students.
http://www.ealnet.com/ealsoft/fracted.htm
Mandelbrot Questions & Answers (without any scary details) by Paul
Derbyshire
http://chat.carleton.ca/~pderbysh/mandlfaq.html
Godric's fractal gallery. A brief introduction to Fractals clear and
well illustrated explanations
http://www.gozen.demon.co.uk/godric/fracgall.html
Lystad Fractal Info complex numbers and fractals
http://www.iglobal.net/lystad/lystad-fractal-info.html
Fractal eXtreme: fractal theory theoritical informations
http://www.cygnus-software.com/theory/theory.htm
Frode Gill Fractal pages mathematical and programming data about
classical fractals and quaternions
http://www.krs.hia.no/~fgill/fractal.html
Fractals: a history
http://graffiti.cribx1.u-bordeaux.fr/MAPBX/louvet/history.html
Basic informations about fractals
http://graffiti.cribx1.u-bordeaux.fr/MAPBX/louvet/jpl1a.html
Fantastic Fractals a very comprehensive site with tutorials for
beginners and more advanced readers, workshops etc.
http://library.advanced.org/12740/cgi-bin/welcome.cgi
Chaos, Fractals, Dimension: mathematics in the age of the computer by
Glenn Elert. A huge (>100 pages double-spaced) essay on
chaos, fractals, and non-linear dynamics. It requires a
moderate math background, though is not aimed at the
mathematician.
http://www.columbia.edu/~gae4/chaos/
Mathsnet this site has several pages devoted to fractals and complex
numbers.
http://www.anglia.co.uk/education/mathsnet/
Fractals in Your Future by Ronald Lewis <ronlewis@sympatico.ca>
http://www.eureka.ca/resources/fiyf/fiyf.html
 
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