Science Television
Chaos, Fractals and Dynamics:
Computer Experiments in Dynamics
by Robert L. Devaney
Copyright 1989
Running time 63 minutes
This video will soon be available as a DVD from CustomFlix of
Amazon.com
Robert Devaney presents the mathematics chaos and illustrated with
computer graphics and animations which are available free on
Google Video
Description
In this captivating and richly illustrated videotape Boston University
mathematics professor Robert L. Devaney communicates his deep
understanding as will as his enthusiasm for the topics of chaos,
fractals and dynamical systems. Starting at a level suitable for
well-prepared high school students, he tells the mathematical story
behind these fascinating topics.
Using attractive graphs and diagrams, Devaney gives a clear and
visually appealing introduction to the concepts. Computer generated
graphics of the fractal Julia sets of the sine, cosine and exponential
functions offer stunning proof of the beauty and complexity of these
subjects. Devaney explains how the computer is used to make the
still pictures and animations.
Though the mathematical background required is elementary, those
at the collegiate level and beyond will appreciate this tape for the
clarity of exposition and the sheer beauty of the graphics.
It can be used by itself or as a companion to Devaney's
Addison-Wesley book of the same title.
Reviews
The Mathematics Teacher, October 1990
This videotape is intended for college freshman mathematics classes
but could have some value in an accelerated high school
mathematics class.
The videotape furnishes an excellent mathematical description of a
concept that most mathematics students have seen only visually.
This mathematical description of iterations and fractals is very
mathematically sound and well sequenced for the viewer. Students
could watch the videotape with no teacher direction and then have a
class discussion afterward. It is nicely divided into two parts to be
used over a two day period.
By showing equations and corresponding fractals and then zooming
in to see what is happening at various places, the tape does
something that is difficult to accomplish in the normal classroom,
even with a computer - it makes the notion of chaos come alive. I
found it very helpful in a calculus class.
James Mason, San Diego State University, San Diego, CA
Mathematical Reviews, issue 92a
This videotape presents two lectures by the author on dynamical
systems theory- particularly, chaotic behavior in such systems. He
begins with a general description of why simple systems may exhibit
complicated behaviour, and then devotes the remainder of the first
lecture to explaining how one can view iterated maps as dynamical
systems. Using mappings of the real line to itself he explains the
graphical the graphical method of tracing out trajectories and then
he exhibits systems with predictable and unpredictable behaviour
The second lecture discusses two-dimensional mappings - in
particular, mappings of the complex plane. After an elementary but
enlightening description of the notion of sensitive dependence on
initial conditions, the author introduces the notion of the Julia set of
a complex function. Much of the rest of the video consists of
computer graphics images produced by the author and co-workers,
showing how the Julia set can change as one varies some parameter
in the function.
The mathematical knowledge required of the viewer is relatively
small - basically just the arithmetic of complex numbers and the
exponential function. Thus, the tape would be suitable for use even
in an advanced high school class. It could also be used in an
elementary ordinary differential equations course to illustrate some
of the modern trends in the theory of dynamical systems.
C. Eugene Wayne (I-PAS)
The American Mathematical Monthly, June-July, 1991
A collage of material on dynamical systems and Julia sets woven
together by a lecture (a "talking head" in the upper right corner of
the screen) that begins with generalities (weather, planets, stock
markets,) and very elementary exercises, but moves quickly to
relatively sophisticated exploration of dynamics in the plane.
Incorporates several of Devaney's short films on Julia sets of various
sine and cosine functions in the complex plane. Illustrates various
types of critical behaviour both with static visuals (slide-like graphs)
and with evolving Julia set films. Although the learning slope from
beginning to end is rather steep, the film can serve to motivate and
illustrate dynamical systems at many different levels.
Lynn A. Steen
