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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

20 November 1924 – 14 October 2010


First Citizen

of

Science

(1924 – 2010)


Father

of

Fractal Geometry

(1924 – 2010)


Theoryof

Roughness

The Fractal

Geometry

of Nature

(1924 – 2010)


1977

1982


1985

December 6, 1982

Leo Kadanoff

University of Utah

The year when I metBenoit MandelbrotandRichard F. Voss



The mathematics behindthe Mandelbrot Set

1986



Publishing all the algorithms known at that time

1988


How Mountains turn into Clouds …

A completely synthetic mathematical

construction of mountains and clouds

A Masterpiece by Richard F. Voss



1991...

PeitgenJürgensSaupe

MaletskyPercianteYunker



Mandelbrot Set:

The most complex object mathematics has ever seen


Iteration

Iteration of rational functions

Theory of Julia & Fatou~1918


Newton's Method for x3-1

I studied thatin the fall of 1982at the University of Utah


Julia Sets

"The iteration does not escape to infinity"

"The Prisoner Set"


z

b

a


z

b

a

1/z


z

b

a





connected

not connected

dust


connected

not connected

Cantor Set

(super) infinite dust








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


1

1/4

-2

-1


The Mandelbrot Set

Making a picture:b/w

all sequences become unbounded"escape"

2

some sequences remain bounded"imprisoned"


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)



Similarity between

Julia Sets

and the

Mandelbrot Set



Mandelbrot Set 1990 (Peitgen/Jürgens/Saupe)

Electrostatic Potential(key for mathematical understanding)





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