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Remembering Benoit Mandelbrot

Remembering Benoit Mandelbrot. 20 November 1924 – 14 October 2010. First Citizen of Science. (1924 – 2010). Father of Fractal Geometry. (1924 – 2010). Theory of Roughness. The Fractal Geometry of Nature. (1924 – 2010). 1977. 1982. 1985. December 6, 1982 Leo Kadanoff

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Remembering Benoit Mandelbrot

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  1. Remembering Benoit Mandelbrot 20 November 1924 – 14 October 2010

  2. First Citizen of Science (1924 – 2010)

  3. Father of Fractal Geometry (1924 – 2010)

  4. Theoryof Roughness The Fractal Geometry of Nature (1924 – 2010)

  5. 1977 1982

  6. 1985 December 6, 1982 Leo Kadanoff University of Utah The year when I metBenoit MandelbrotandRichard F. Voss

  7. Mandelbrot Set 1980

  8. The mathematics behindthe Mandelbrot Set 1986

  9. University of California at Santa Cruz, October 1987

  10. Publishing all the algorithms known at that time 1988

  11. How Mountains turn into Clouds … A completely synthetic mathematical construction of mountains and clouds A Masterpiece by Richard F. Voss

  12. 1991...

  13. 1991... PeitgenJürgensSaupe MaletskyPercianteYunker

  14. 1992

  15. Mandelbrot Set: The most complex object mathematics has ever seen

  16. Iteration Iteration of rational functions Theory of Julia & Fatou~1918

  17. Newton's Method for x3-1 I studied thatin the fall of 1982at the University of Utah

  18. Julia Sets "The iteration does not escape to infinity" "The Prisoner Set"

  19. z b a

  20. z b a 1/z

  21. z b a

  22. Julia Set

  23. Theorem of Julia & Fatou

  24. Theorem of Julia & Fatou

  25. connected not connected dust

  26. connected not connected Cantor Set (super) infinite dust

  27. Two simple Julia Sets

  28. Two simple Julia Sets 1

  29. Two simple Julia Sets 1

  30. Two simple Julia Sets -2 +2

  31. Two simple Julia Sets -2 +2

  32. The Mandelbrot Set

  33. The Mandelbrot Set Computer (Pixel) Graphics Making a picture:(b/w) sequence becomes unbounded"escapes" C64: 1982 16 colors Macintosh: 1984 b/w--------------------------RGB 256x256x256only in few research labsUniversity of Utah sequence remains bounded"imprisoned" 1980

  34. 1 1/4 -2 -1

  35. The Mandelbrot Set Making a picture:b/w all sequences become unbounded"escape" 2 some sequences remain bounded"imprisoned"

  36. 1982/83Salt Lake City The Mandelbrot Set "escapes"takes 13 steps to landoutside circle "escapes"takes 5 steps to landoutside circle "imprisoned" 2 Making a picture:(color)

  37. Around the Mandelbrot Set Powers of Ten

  38. Similarity between Julia Sets and the Mandelbrot Set

  39. 1/(period)2

  40. Mandelbrot Set 1990 (Peitgen/Jürgens/Saupe) Electrostatic Potential(key for mathematical understanding)

  41. Flying the Mandelbrot Set

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