Remembering benoit mandelbrot
Download
1 / 52

Remembering Benoit Mandelbrot - PowerPoint PPT Presentation


  • 218 Views
  • Uploaded on
  • Presentation posted in: General

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha

Download Presentation

Remembering Benoit Mandelbrot

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


Mandelbrot Set 1980


The mathematics behindthe Mandelbrot Set

1986


University of California at Santa Cruz, October 1987


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...


1991...

PeitgenJürgensSaupe

MaletskyPercianteYunker


1992


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


Julia Set


Theorem of Julia & Fatou


Theorem of Julia & Fatou


connected

not connected

dust


connected

not connected

Cantor Set

(super) infinite dust


Two simple Julia Sets


Two simple Julia Sets

1


Two simple Julia Sets

1


Two simple Julia Sets

-2

+2


Two simple Julia Sets

-2

+2


The Mandelbrot Set


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)


Around the Mandelbrot Set

Powers of Ten


Similarity between

Julia Sets

and the

Mandelbrot Set


1/(period)2


Mandelbrot Set 1990 (Peitgen/Jürgens/Saupe)

Electrostatic Potential(key for mathematical understanding)


Flying the Mandelbrot Set


Interview Bremen1986


We will always remember


ad
  • Login