Fractals, Graphics, and Mathematics Education

Part I. Introductory Essays: 1. Some reasons for the effectiveness of fractal geometry in mathematics education Benoit B. Mandelbrot and Michael Frame; 2. Unsolved problems and still emerging concepts Benoit B. Mandelbrot; 3. Fractals, graphics and mathematics education Benoit B. Mandelbrot; 4. Mathematics and society in the twentieth century Benoit B. Mandelbrot; Part II. Classroom Experiences: 5. Teaching fractals and dynamical systems at the Hotchkiss school Melkana Brakalova and David Coughlin; 6. Reflection on Wada basins: some fractals with a twist Dane Camp; 7. Learning and teaching about fractals Donald M. Davis; 8. The fractal geometry of the Mandelbrot set Robert L. Devaney; 9. Fractals - energizing the mathematics classroom Viki Fegers and Mary Beth Johnson; 10. Other chaos games Sandy Fillebrown; 11. Creating and teaching undergraduate courses in fractal geometry: a personal experience Michel Lapidus; 12. Exploring Fractal dimensions by experiment Ron Lewis; 13. Fractal themes on all levels Kenneth G. Monks; 14. Art and fractals: artistic explorations of natural self-similarity Brianna Murati and Michael Frame; 15. Order and chaos, art and magic: a first college course in quantitative reasoning based on fractals and chaos David Peak and Michael Frame; 16. A software driven undergraduate fractals course Douglas C. Ravenel; Part III. A Final Word: 17. The fractal ring from art to art through mathematics, finance and the sciences Benoit B. Mandelbrot; Part IV. Appendices: 18. Panorama of fractals and their uses. An alphabetic workbook-index Michael Frame and Benoit B. Mandelbrot; 19. Reports of some field experiences.