Benoît Mandelbrot

Benoît B. Mandelbrot
Ilustracja
Benoît Mandelbrot na konferencji TED (2010)
Państwo działania

 Francja
 Stany Zjednoczone

Data i miejsce urodzenia

20 listopada 1924
Warszawa

Data i miejsce śmierci

14 października 2010
Cambridge, Massachusetts

Doktor nauk matematyka, aerodynamika
Alma Mater

École polytechnique
California Institute of Technology

Doktorat

1952 – matematyka
Uniwersytet Paryski

Uczelnia

Uniwersytet Paryski

Odznaczenia
Oficer Orderu Narodowego Legii Honorowej (Francja)
2003 Nagroda Japońska
1993 Nagroda Wolfa (fizyka)
1989 Harvey Prize
1986 Franklin Medal
1985 Barnard Medal

Benoît B. Mandelbrot, imię przy narodzeniu: Benedykt[1] (ur. 20 listopada 1924 w Warszawie, zm. 14 października 2010 w Cambridge, Massachusetts) – francuski i amerykański matematyk[2][3] polsko-żydowskiego pochodzenia. Zajmował się szerokim zakresem problemów matematycznych, znany jest przede wszystkim jako ojciec geometrii fraktalnej, opisał zbiór Mandelbrota oraz wymyślił samo słowo „fraktal”.

Bratanek Szolema Mandelbrojta[1].

Życiorys

Urodził się w rodzinie litewskich Żydów mieszkających po I wojnie światowej w Polsce, jako syn lekarki i handlarza odzieżą[1]. W latach 1924–1936 mieszkał w Polsce, a w latach 1936–1957 we Francji. Pracował w Centre national de la recherche scientifique w Paryżu, a następnie na Uniwersytecie w Lille. Od 1957 pracował w USA dla firmy IBM, miał zatem dostęp do najnowocześniejszych komputerów. Mandelbrot dotarł do prac dwóch francuskich matematyków: Gastona Julii i Pierre’a Fatou, którzy badali zachowanie się iteracji pewnych funkcji zespolonych. Wykorzystał do tego celu komputery. Uzyskane przez niego wykresy zostały nazwane fraktalami.

W 1993 został uhonorowany Nagrodą Wolfa w fizyce, a w 2003 został wyróżniony prestiżową Nagrodą Japońską. Otrzymał 16 tytułów doktora honoris causa[4] oraz inne wyróżnienia, m.in. Medal im. Wacława Sierpińskiego[5].

Zmarł w hospicjum w Cambridge (Massachusetts) na raka trzustki[6].

Fraktale

Seria kolejnych powiększeń zbioru Mandelbrota
Mandel zoom 00 mandelbrot set.jpg
Mandel zoom 01 head and shoulder.jpg
Mandel zoom 02 seehorse valley.jpg
Mandel zoom 03 seehorse.jpg
Mandel zoom 04 seehorse tail.jpg
Mandel zoom 05 tail part.jpg
Mandel zoom 06 double hook.jpg
Mandel zoom 07 satellite.jpg
Mandel zoom 08 satellite antenna.jpg
Mandel zoom 09 satellite head and shoulder.jpg
Mandel zoom 10 satellite seehorse valley.jpg
Mandel zoom 11 satellite double spiral.jpg
Mandel zoom 12 satellite spirally wheel with julia islands.jpg
Mandel zoom 13 satellite seehorse tail with julia island.jpg
Mandel zoom 14 satellite julia island.jpg
Mandel zoom 15 one island.jpg
Mandel zoom 16 spiral island.jpg


Przypisy

  1. ↑ a b c Zofia Gołąb-Meyer. Benoit Mandelbrot (1924–2010) – ojciec geometrii fraktalnej. „Foton”. 112, s. 50, Wiosna 2011. Instytut Fizyki Uniwersytetu Jagiellońskiego. 
  2. ↑ Benoit B. Mandelbrot Biography. Bookrags. [dostęp 2017-09-09]. (ang.).
  3. ↑ Mandelbrot Benoît B., [w:] Encyklopedia PWN [online] [dostęp 2017-09-09].
  4. ↑ Marek Matacz. Pan od fraktali. „Wiedza i Życie”. 7/2010. s. 60–63. 
  5. ↑ Medal i Wykład im. Wacława Sierpińskiego na stronie PTM, https://www.ptm.org.pl/konkursy/wyklady-im-waclawa-sierpinskiego.
  6. ↑ Jascha Hoffman: Benoit Mandelbrot, Novel Mathematician, Dies at 85. The New York Times, 2010-10-16. [dostęp 2017-09-09]. (ang.).

Linki zewnętrzne

Laureaci Nagrody Wolfa w dziedzinie fizyki
XX wiek
XXI wiek

Wolf prize icon.png

Laureaci Medalu im. Wacława Sierpińskiego
XX wiek
XXI wiek
Laureaci Nagrody Japońskiej
XX wiek
XXI wiek

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Media użyte na tej stronie

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The flag of Navassa Island is simply the United States flag. It does not have a "local" flag or "unofficial" flag; it is an uninhabited island. The version with a profile view was based on Flags of the World and as a fictional design has no status warranting a place on any Wiki. It was made up by a random person with no connection to the island, it has never flown on the island, and it has never received any sort of recognition or validation by any authority. The person quoted on that page has no authority to bestow a flag, "unofficial" or otherwise, on the island.
Japan Prize logo.svg
Logo of The Japan Prize Foundation.
Mandel zoom 04 seehorse tail.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 4 of a zoom sequence: The central endpoint of the "seahorse tail" is also a Misiurewicz point.
  • Coordinates of the center: Re(c) = -.743,566,9, Im(c) = . 131,402,3
  • Horizontal diameter of the image: .002,287,8
  • Magnification relative to the initial image: 1,344.9
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Wolf prize icon.png
An icon designating the Wolf Foundation logo. Note, that the icon is not a small copy of the Wolf's logo: it was simplified (lost some curves) for legibility.
Mandel zoom 16 spiral island.jpg
Mandelbrot set zoom step 16. Just beyond File:Mandel zoom 15 one island.jpg. Retrieved from [1].
Mandel zoom 14 satellite julia island.jpg
Autor: Wolfgang Beyer, Licencja: CC-BY-SA-3.0
* Partial view of the Mandelbrot set. Step 14 of a zoom sequence: On the first sight these islands seem to consist on infinitely many parts like Cantor sets, as it is actually the case for the corresponding Julia set Jc. Here they are connected by tiny structures so that the whole represents a simply connected set. These tiny structures meet each other at a satellite in the center which is too small to be recognized at this magnification. The value of c for the corresponding Jc is not that of the image center but has relative to the main body of the Mandelbrot set the same position as the center of this image relative to the satellite shown in zoom step 7.
  • Coordinates of the center: Re(c) = -.743,643,887,037,151, Im(c) = .131,825,904,205,330
  • Horizontal diameter of the image: .000,000,000,051,299
  • Magnification relative to the initial image: 59,979,000,000
Benoit Mandelbrot, TED 2010.jpg
Autor: Steve Jurvetson, Licencja: CC BY 2.0
Benoit Mandelbrot talking at TED (Technology, Entertainment, Design) conference
Mandel zoom 09 satellite head and shoulder.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 9 of a zoom sequence: The "seahorse valley" of the satellite. All the structures from the image of zoom step 1 reappear.
  • Coordinates of the center: Re(c) = -.743,644,099,61, Im(c) = .131,826,046,88
  • Horizontal diameter of the image: .000,000,662,08
  • Magnification relative to the initial image: 4,647,300
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 10 satellite seehorse valley.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 10 of a zoom sequence: Double-spirals and "seahorses". Unlike the image of zoom step 2 they have appendices consisting of structures like "seahorse tails". This demonstrates the typical linking of n+1 different structures in the environment of satellites of the order n, here for the simplest case n=1.
  • Coordinates of the center: Re(c) = -.743,643,862,69, Im(c) = .131,825,902,71
  • Horizontal diameter of the image: .000,000,135,26
  • Magnification relative to the initial image: 22,748,000
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 02 seehorse valley.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 2 of a zoom sequence: On the left double-spirals, on the right "seahorses".
  • Coordinates of the center: Re(c) = -.759,856, Im(c) = .125,547
  • Horizontal diameter of the image: .051,579
  • Magnification relative to the initial image: 59,654
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 00 mandelbrot set.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Mandelbrot set. Initial image of a zoom sequence: Mandelbrot set with continuously colored environment.
  • Coordinates of the center: Re(c) = -.7, Im(c) = 0
  • Horizontal diameter of the image: 3.076,9
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 05 tail part.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 5 of a zoom sequence: Part of the "tail". There is only one path consisting of the thin structures which leads through the whole "tail". This zigzag path passes the "hubs" of the large objects with 25 "spokes" on the inner and outer sides of the "tail". It makes sure, that the Mandelbrot set is a so called simply connected set. That means there are no islands and no loop roads around a hole.
  • Coordinates of the center: Re(c) = -.743,649,90, Im(c) = . 131,882,04
  • Horizontal diameter of the image: .000,738,01
  • Magnification relative to the initial image: 4,169.2
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 08 satellite antenna.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 8 of a zoom sequence: "Antenna" of the satellite. Several satellites of second order can be recognized.
  • Coordinates of the center: Re(c) = -.743,644,786,0, Im(c) = .131,825,253,6
  • Horizontal diameter of the image: .000,002,933,6
  • Magnification relative to the initial image: 1,048,800
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 06 double hook.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 6 of a zoom sequence: Satellite. The two "seahorse tails" are the beginning of a series of concentrical crowns with the satellite in the center.
  • Coordinates of the center: Re(c) = -.743,640,85, Im(c) = .131,827,33
  • Horizontal diameter of the image: .000,120,68
  • Magnification relative to the initial image: 25,497
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 11 satellite double spiral.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 4 of a zoom sequence: The central endpoint of the "seahorse tail" is also a Misiurewicz point.
  • Coordinates of the center: Re(c) = -.743,643,900,055, Im(c) = .131,825,890,901
  • Horizontal diameter of the image: .000,000,049,304
  • Magnification relative to the initial image: 62,407,000
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 13 satellite seehorse tail with julia island.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 13 of a zoom sequence: Part of the "double-hook".
  • Coordinates of the center: Re(c) = -.743,643,887,173,42, Im(c) = .131,825,904,251,82
  • Horizontal diameter of the image: .000,000,000,598,49
  • Magnification relative to the initial image: 5,141,100,000
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 12 satellite spirally wheel with julia islands.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 12 of a zoom sequence: In the outer part of the appendices islands of structures can be recognized. They have a shape like Julia sets Jc. The largest of them can be found in the center of the "double-hook" on the right side.
  • Coordinates of the center: Re(c) = -.743,643,888,570,6, Im(c) = .131,825,904,312,4
  • Horizontal diameter of the image: .000,000,004,149,3
  • Magnification relative to the initial image: 741,550,000
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 01 head and shoulder.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 1 of a zoom sequence: Gap between the "head" and the "body" also called the "seahorse valley".
  • Coordinates of the center: Re(c) = -.875,91, Im(c) = .204,64
  • Horizontal diameter of the image: .531,84
  • Magnification relative to the initial image: 5.785,4
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 07 satellite.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 7 of a zoom sequence: Each of these crowns consists of similar "seahorse tails". Their number increases with powers of 2, a typical phenomenon in the environment of satellites. The unique path to the spiral center mentioned in zoom step 5 passes the satellite from the groove of the cardioid to the top of the "antenna" on the "head". Also observe that the starting view is located in the center.
  • Coordinates of the center: Re(c) = -.743,643,135, Im(c) = .131,825,963
  • Horizontal diameter of the image: .000,014,628
  • Magnification relative to the initial image: 210,350
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.
Mandel zoom 03 seehorse.jpg
Autor: Created by Wolfgang Beyer with the program Ultra Fractal 3., Licencja: CC-BY-SA-3.0
Partial view of the Mandelbrot set. Step 3 of a zoom sequence: "Seahorse" upside down. Its "body" is composed by 25 "spokes" consisting of 2 groups of 12 "spokes" each and one "spoke" connecting to the main cardioid. These 2 groups can be attributed by some kind of metamorphosis to the 2 "fingers" of the "upper hand" of the Mandelbrot set. Therefore the number of "spokes" increases from one "seahorse" to the next by 2. The "hub" is a so called Misiurewicz point. Between the "upper part of the body" and the "tail" a distorted satellite can be recognized.
  • Coordinates of the center: Re(c) = -.743,030, Im(c) = .126,433
  • Horizontal diameter of the image: .016,110
  • Magnification relative to the initial image: 190.99
  • Created by Wolfgang Beyer with the program Ultra Fractal 3.
  • Uploaded by the creator.