Remembering benoit mandelbrot
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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

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Remembering benoit mandelbrot

Remembering

Benoit

Mandelbrot

20 November 1924 – 14 October 2010


Remembering benoit mandelbrot

First Citizen

of

Science

(1924 – 2010)


Remembering benoit mandelbrot

Father

of

Fractal Geometry

(1924 – 2010)


Remembering benoit mandelbrot

Theoryof

Roughness

The Fractal

Geometry

of Nature

(1924 – 2010)


Remembering benoit mandelbrot

1977

1982


Remembering benoit mandelbrot

1985

December 6, 1982

Leo Kadanoff

University of Utah

The year when I metBenoit MandelbrotandRichard F. Voss


Remembering benoit mandelbrot

Mandelbrot Set 1980


Remembering benoit mandelbrot

The mathematics behindthe Mandelbrot Set

1986


Remembering benoit mandelbrot

University of California at Santa Cruz, October 1987


Remembering benoit mandelbrot

Publishing all the algorithms known at that time

1988


Remembering benoit mandelbrot

How Mountains turn into Clouds …

A completely synthetic mathematical

construction of mountains and clouds

A Masterpiece by Richard F. Voss


Remembering benoit mandelbrot

1991...


Remembering benoit mandelbrot

1991...

PeitgenJürgensSaupe

MaletskyPercianteYunker


Remembering benoit mandelbrot

1992


Remembering benoit mandelbrot

Mandelbrot Set:

The most complex object mathematics has ever seen


Remembering benoit mandelbrot

Iteration

Iteration of rational functions

Theory of Julia & Fatou~1918


Remembering benoit mandelbrot

Newton's Method for x3-1

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


Remembering benoit mandelbrot

Julia Sets

"The iteration does not escape to infinity"

"The Prisoner Set"


Remembering benoit mandelbrot

z

b

a


Remembering benoit mandelbrot

z

b

a

1/z


Remembering benoit mandelbrot

z

b

a


Remembering benoit mandelbrot

Julia Set


Remembering benoit mandelbrot

Theorem of Julia & Fatou


Remembering benoit mandelbrot

Theorem of Julia & Fatou


Remembering benoit mandelbrot

connected

not connected

dust


Remembering benoit mandelbrot

connected

not connected

Cantor Set

(super) infinite dust


Remembering benoit mandelbrot

Two simple Julia Sets


Remembering benoit mandelbrot

Two simple Julia Sets

1


Remembering benoit mandelbrot

Two simple Julia Sets

1


Remembering benoit mandelbrot

Two simple Julia Sets

-2

+2


Remembering benoit mandelbrot

Two simple Julia Sets

-2

+2


Remembering benoit mandelbrot

The Mandelbrot Set


Remembering benoit mandelbrot

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


Remembering benoit mandelbrot

1

1/4

-2

-1


Remembering benoit mandelbrot

The Mandelbrot Set

Making a picture:b/w

all sequences become unbounded"escape"

2

some sequences remain bounded"imprisoned"


Remembering benoit mandelbrot

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)


Remembering benoit mandelbrot

Around the Mandelbrot Set

Powers of Ten


Remembering benoit mandelbrot

Similarity between

Julia Sets

and the

Mandelbrot Set


Remembering benoit mandelbrot

1/(period)2


Remembering benoit mandelbrot

Mandelbrot Set 1990 (Peitgen/Jürgens/Saupe)

Electrostatic Potential(key for mathematical understanding)


Remembering benoit mandelbrot

Flying the Mandelbrot Set


Remembering benoit mandelbrot

Interview Bremen1986


Remembering benoit mandelbrot

We will always remember


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