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Dynamical Systems and Fractals: Computer Graphics Experiments with Pascal

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This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST.

The story which today so fascinates researchers, and which is associated with chaos
theory and experimental mathematics, came to our attention around 1983 in Bremen. At
that time a research group in dynamical systems under the leadership of Professors
Peitgen and Richter was founded at Bremen University. This starting-point led to a
collaboration lasting many years with members of the Computer Graphics Laboratory at
the University of Utah in the USA.

Equipped with a variety of research expertise, the research group began to install its
own computer graphics laboratory. In January and February of 1984 they made their
results public. These results were startling and caused a great sensation. For what they
exhibited was beautiful, coloured computer graphics reminiscent of artistic paintings. The
first exhibition, Harmony in Chaos and Cosmos, was followed by the exhibition
Moqhology of Complex Frontiers. With the next exhibition the results became
internationally known. In 1985 and 1986, under the title Frontiers of Chaos and with
assistance from the Goethe Institute, this third exhibition was shown in the UK and the
USA. Since then the computer graphics have appeared in many magazines and on
television, a witches’ brew of computer-graphic simulations of dynamical systems.
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