Written by the award winning authors of Chaos and Fractals (0-387-97903-4), this work introduces the reader to iterated function systems through a lively, interactive approach. This well-written, clearly illustrated book explores the history and the unlimited potential of fractals, while developing a basic mathematical understanding and appreciation for the topics.

There are many reasons for writing this first volume of strategic activities on fractals. The most pervasive is the compelling desire to provide students of mathematics with a set of accessible, hands-on experiences with fractals and their underlying mathematical principles and characteristics. Another is to show how fractals connect to many different aspects of mathematics and how the study of fractals can bring these ideas together. A third is to share the beauty of their structure and shape both through what the eye sees and what the mind visualizes. Fractals have captured the attention, enthusiasm, and interest of many people around the world. To the casual observer, their color, beauty, and geometric structure captivates the visual senses like few other things they have ever experienced in mathematics. To the computer scientist, fractals offer a rich environment in which to explore, create, and build a new visual world as an artist creating a new work. To the student, fractals bring mathematics out of past history and into the twenty-first century. To the mathematics teacher, fractals offer a unique, new opportunity to illustrate both the dynamics of mathematics and its many connecting links.

The same factors that motivated the writing of our first volume of strategic activities on fractals continued to encourage the assembly of additional activities for this second volume. Fractals provide a setting wherein students can enjoy hands-on experiences that involve important mathematical content connected to a wide range of physical and social phenomena. The striking graphic images, unexpected geometric properties, and fascinating numerical processes offer unparalleled opportunity for enthusiastic student inquiry. Students sense the vigor present in the growing and highly integrative discipline of fractal geom etry as they are introduced to mathematical developments that have occurred during the last half of the twentieth century. Few branches of mathematics and computer science offer such a contem porary portrayal of the wonderment available in careful analysis, in the amazing dialogue between numeric and geometric processes, and in the energetic interaction between mathematics and other disciplines. Fractals continue to supply an uncommon setting for animated teaching and learn ing activities that focus upon fundamental mathematical concepts, connections, problem-solving techniques, and many other major topics of elementary and advanced mathematics. It remains our hope that, through this second volume of strategic activities, readers will find their enjoyment of mathematics heightened and their appreciation for the dynamics of the world in creased. We want experiences with fractals to enliven curiosity and to stretch the imagination."

Das vorliegende Arbeitsbuch ist Teil eines Paketes von verschiedenen Materialien, die das Ziel haben, das Thema Chaos und Fraktale in den mathematisch-naturwissenschaftlichen Unterricht einzufuhren. Ein weiteres Anliegen besteht darin, das mentale Bild von Mathematik im Bewusstsein der Schuler attraktiver zu gestalten. Mathematik ist die Antwort des Menschen auf die Komplexitat der Welt. Mathematik ist die Ordnungsmacht im Dschungel der Phanomene. Deshalb ist Mathematik le bendig, frisch und aktuell. Deshalb gibt es zwischen einzelnen Teilgebieten und Ergebnissen der Mathematik immer wieder uberraschende Querverbindungen, die oft das Verstandnis einer Sache erst wirklich erhellen. Und deshalb bietet es sich an, durch entdeckendes, explorierendes Lernen die Anziehungskraft dieser Eigenschaften der Mathematik im Unterricht auszunutzen. Chaos und Fraktale bieten hierfur eine besondere neue Chance. Beide sind jung und aktuell und belegen so ohne weiteres, dass Mathematik lebt. Fur beide gilt, dass einige ihrer schrittmachenden Entdeckungen nicht ohne Hilfe von Computern moeglich gewesen waren. Damit rucken faszinie rende Computerexperimente naturlich in den Mittelpunkt. Beide sind hochgradig interdisziplinar. Dieses heisst, dass gehaltvolle Anwendungen nicht erst muhsam konstruiert werden mussen. Beide behandeln Themen, die von sich aus wirken. Tatsachlich durchlaufen seit Ende der siebziger Jahre Mathematik und Naturwissenschaften eine Welle, die in ihrer Kraft, Kreativitat und Weitraumigkeit langst ein interdisziplinares Ereignis er sten Ranges geworden ist. Das andauernde Interesse innerhalb und ausserhalb der Wissenschaften ist in einer aufruttelnden Betroffenheit begrundet, die eine radikale Wende in dem uberkommenen naturwissenschaftlichen Weltbild und manchen uberdehnten Interpretationen ankundigt.