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Beauty of Fractals

Denny Gulick and Jon Scott

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Fractals came onto the stage in the 1970's with the emergence of the Mandelbrot set, with its incredibly complicated and interesting boundary. During the 1980's a number of books appeared — including most especially by Mandelbrot, Barnsley and Devaney — that gave a mathematical background for fractals that made fractals accessible to both students and teachers. More recently, as computers and their users have become more sophisticated, the domain of fractals has broadened, from art to scientific application to mathematical analysis. In particular, students in high school as well as college are often introduced to fractals and fractal concepts. The Beauty of Fractals: Six Different Views includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject.

The six essays appearing in this book can be grouped as follows. The first two have a more descriptive nature, the first in terms of pictorial images that are fractal and the second in terms of fractals that appear in the famous stage play Arcadia. The third, fourth and fifth essays are devoted to the famous classical fractals and their close relatives. The sixth essay connects differential equations to fractals. Although the final two essays may appear to be a bit more sophisticated than the others, we observe that they are co-authored with undergraduate students. We note that each of the six essays is self-contained and expository, and is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that do not usually appear in textbooks on fractals.

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Electronic ISBN: 9780883859711

Print ISBN: 9780883851869

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