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Topic: Sierpinski carpet


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In the News (Sun 18 Aug 19)

  
  Wacław Sierpiński - Wikipedia, the free encyclopedia
In 1907 that Sierpinski first became interested in set theory when he came across a theorem which stated that points in the plane could be specified with a single coordinate.
Sierpinski began to study set theory and, in 1909, he gave the first ever lecture course devoted entirely to the subject.
Waclaw Sierpinski is interred in the Powązki Cemetery, Warsaw, Poland.
en.wikipedia.org /wiki/Waclaw_Sierpinski   (800 words)

  
 Waclaw Sierpinski
Two well-known fractals are named after him (the Sierpinski triangle and the Sierpinski carpet), as are Sierpinski numbers and the associated Sierpinski problem.
Sierpinski enrolled in the Department of Mathematics and Physics at the University of Warsaw in 1899 and graduated four years later.
Waclaw Sierpinski is interred in the Powazki Cemetery, Warsaw, Poland.
publicliterature.org /en/wikipedia/w/wa/waclaw_sierpinski.html   (787 words)

  
 Sierpinski carpet - Wikipedia, the free encyclopedia
The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński.
The carpet is one generalization of the Cantor set to two dimensions (the other is Cantor dust).
Martin Barlow and Richard Bass have shown that a random walk on the Sierpinski carpet diffuses at a slower rate than an unrestricted random walk in the plane.
en.wikipedia.org /wiki/Sierpinski_carpet   (243 words)

  
 Sierpinski triangle - Wikipedia, the free encyclopedia
The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis, (first image).
The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.
The tetrix is the three-dimensional analog of the Sierpinski triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process.
en.wikipedia.org /wiki/Sierpinski_triangle   (674 words)

  
 Sierpinski Carpet
The Sierpinski carpet is the intersection of all the sets in this sequence, that is, the set of points that remain after this construction is repeated infintely often.
Sierpinski used the carpet to catalogue all compact one-dimensional objects in the plane (from a topological point of view).
So the Sierpinski carpet was actually invented by Stefan Mazurkiewicz, who in 1913 wrote his Ph.D. thesis under the supervision of Sierpinski on curves filling a square.
ecademy.agnesscott.edu /~lriddle/ifs/carpet/carpet.htm   (523 words)

  
 Encyclopedia: Sierpinski carpet
The Sierpinski carpet, named after Wacław Sierpiński, is a fractal derived from a square by cutting it into 9 equal squares with a 3-by-3 grid, removing the central piece and then applying the same procedure ad infinitum to the remaining 8 squares.
For an HTML approach of approximating a Sierpinski carpet, see dive into mark.
Categories: Fractals The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, named after Waclaw Sierpinski.
www.nationmaster.com /encyclopedia/Sierpinski-carpet   (561 words)

  
 Sierpinski Gasket   (Site not responding. Last check: 2007-11-06)
Closely related to the gasket is the Sierpinski carpet.
The dimension of the carpet is log 8 / log 3 = 1.8928.
The sponge is the 3 dimensional form of the 2D carpet.
astronomy.swin.edu.au /~pbourke/fractals/gasket   (1697 words)

  
 Fractals: Sierpinski Objects
Intuitively, the length of the Sierpinski gasket is the total of the length of all the segments required to draw the object.
This was a period of Russian occupation of Poland and despite the difficulties, Sierpinski entered the Department of Mathematics and Physics of the University of Warsaw in 1899.
Sierpinski graduated in 1904 and worked for a while as a school teacher of mathematics and physics in a girls school in Warsaw.
users.skynet.be /TGMDev/curvesierpinskiobj.htm   (1475 words)

  
 Sierpinski carpet -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-06)
A three-dimensional version of the Sierpinski carpet is the (Click link for more info and facts about Menger sponge) Menger sponge, invented by (Click link for more info and facts about Karl Menger) Karl Menger and sometimes mistakenly called a Sierpinski sponge.
For an (A set of tags and rules (conforming to SGML) for using them in developing hypertext documents) HTML approach of approximating a Sierpinski carpet, see.
Martin Barlow and Richard Bass have shown that this random walk diffuses in a rate slower than usual random walk: if a usual random walk is after n steps in a distance of then random walk on the discrete Sierpinski carpet reaches only distance for some.
www.absoluteastronomy.com /encyclopedia/s/si/sierpinski_carpet.htm   (316 words)

  
 [No title]
Sierpinski attended the University of Warsaw in 1899, when all classes were taught in Russian.
The fractal dimension of the Sierpinski gasket is df= log3/log2.
The Sierpinki carpet is generated in close analogy to the Sierpinski gasket.
www.facstaff.bucknell.edu /udaepp/090/w3/toddw.htm   (1394 words)

  
 Sierpinski gasket och carpet   (Site not responding. Last check: 2007-11-06)
Sierpinski triangeln, som Sierpinski gasket även kallas, konstrueras utifrån en svart, fylld, triangel.
Sierpinski carpet är de punkter som är kvar efter att ovan beskriva procedur har utförts ett oändligt antal gånger (se bild 3).
Vad Sierpinski försökte göra var att finna en skapelse, i vilken alla endimensionella objekt i planet gick att finna, i någon av sina, topologiskt sätt likadana, former.
www.ludat.lth.se /~dat01hed/sierpinski.html   (870 words)

  
 Sierpinski Gasket
The Sierpinski gasket, also known as the Sierpinski triangle, is the intersection of all the sets in this sequence, that is, the set of points that remain after this construction is repeated infinitely often.
The Sierpinski gasket is also referred to as the Sierpinski triangle or as the Sierpinski triangle curve.
It apparently was Mandelbrot who first gave it the name "Sierpinski's gasket." Sierpinski described the construction to give an example of "a curve simultaneously Cantorian and Jordanian, of which every point is a point of ramification." Basically, this means that it is a curve that crosses itself at every point.
ecademy.agnesscott.edu /~lriddle/ifs/siertri/siertri.htm   (818 words)

  
 Carpet Store   (Site not responding. Last check: 2007-11-06)
Carpet is also the name of a solitaire card game.'' A carpet is any loom-woven, felted textile or grass floor covering.
The Crusades brought Turkish carpets to all of Europe, where they were primarily hung on walls or used on tables.
Historically, however, some have distinguished between carpet and rug based on size (the former being larger) or use (carpets on floors, rugs on beds or on the hearth).
www.awonky.com /pages2/15/carpet-store.html   (1394 words)

  
 Patterned Carpet   (Site not responding. Last check: 2007-11-06)
The term was also used for table and wall coverings, as carpets were not commonly used on the floor in European interiors until the 18th century.
of six iterations.]].]] The Sierpinski carpet, named after Waclaw Sierpinski, is a fractal derived from a square by cutting it into 9 equal squares with a 3-by-3 grid, removing the central piece and then applying the same procedure ad infinitum to the remaining 8 squares.
The Bradford Carpet was made in the late 17th century and was originally belonged to the Earl of Bradford at Castle Bromwich.
www.blownspeakers.com /pages3/66/patterned-carpet.html   (1394 words)

  
 carpet.html   (Site not responding. Last check: 2007-11-06)
The carpets were displayed at The Latin School of Chicago's "Middle School Festival Night" which is held on a Tuesday evening each March.
The first carpet was made on a square piece of canvas which was initially painted fl.
The second carpet, "Variations on Sierpinski's Carpet" began with a white piece of canvas.
homepage.mac.com /tcanright/carpet/carpet.html   (231 words)

  
 Waclaw Sierpinski
Waclaw Sierpinski was born on March 14, 1882, in Warsaw, Poland.
From 1908 to 1914 Sierpinski lectured at the University of Lvov, followed by three years at the University of Moscow.
Sierpinski's most important mathematical work was in the areas of set theory, point set topology, and number theory.
ecademy.agnesscott.edu /~lriddle/ifs/siertri/sierbio.htm   (173 words)

  
 Sierpinski Carpet   (Site not responding. Last check: 2007-11-06)
Sierpinski Carpet is an example of a fractal cluster, which can be formed by The Sierpinski Carpet starts with a square, which is divided into 9 smaller
Sierpinski carpet Sierpinski carpet of using a L-system of six iterations.
Sierpinski carpet of using a Iterated function system The Sierpinski carpet, named after Waclaw Sierpinski, is
www.acquired-knowledge-124.info /sierpinski-carpet.html   (327 words)

  
 Sierpinski curve   (Site not responding. Last check: 2007-11-06)
The Sierpinski curve is a base motif fractal where the base is a square.
The curve is also known as the Sierpinski (universal plane) curve, Sierpinski square or the Sierpinski carpet.
The curve is the only plane locally connected one-dimensional continuum S such that the boundary of each complementary domain of S is a simple closed curve and no two of these complementary domain boundaries intersect.
www.2dcurves.com /fractal/fractals.html   (241 words)

  
 Dimensions For Sierpinski Carpet - Big Carpet Guide
Thus we now have three different dimensions for Sierpinski carpet : a Euclidean dimension (E) of 2, a topological dimension (T) of 1, and a Hausdorff...
A fractal, named after Waclaw Sierpinski, that is derived from a square by cutting it into...
Focusing on the Sierpinski carpet with Ising spins, we are able to obtain...
www.bigcarpetguide.com /dimensions-for-sierpinski-carpet.html   (458 words)

  
 Sierpinskis Carpet   (Site not responding. Last check: 2007-11-06)
Sierpinski, sem heita Teppi Sierpinskis (Sierpinski's Carpet) og Pakkning Sierpinskis (Sierpinski's Gasket).
The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, See also.
But really they are "square Sierpinskis", because Sierpinski carpet is not like ordinary carpet.
www.theofficialscoop23.info /sierpinskis-carpet.html   (274 words)

  
 Chaos and Fractals in Financial Markets, Part 3, by J. Orlin Grabbe   (Site not responding. Last check: 2007-11-06)
To be consistent, then, we must say with respect to the Sierpinski carpet, which is made up of an infinite number of disconnected loops, each of one dimension, that it has a topological dimension of one.
But, once we measure all the holes in the carpet, we discovered that what we are left with is carpet that has been entirely consumed by holes.
If instead we have a Sierpinski carpet that is 9 on each side, then to calculate the "area", we note that the number of Sierpinski copies of the initial square which has a side of length 1 is (dividing each side into r = 9 parts) N = r
www.orlingrabbe.com /Chaos3.htm   (4169 words)

  
 Read about Sierpinski carpet at WorldVillage Encyclopedia. Research Sierpinski carpet and learn about Sierpinski carpet ...   (Site not responding. Last check: 2007-11-06)
Research Sierpinski carpet and learn about Sierpinski carpet here!
It is one generalization of the Cantor set to two dimensions (the other is
For an HTML approach of approximating a Sierpinski carpet, see
encyclopedia.worldvillage.com /s/b/Sierpinski_carpet   (279 words)

  
 What (Sierpinski's Carpet)   (Site not responding. Last check: 2007-11-06)
This activity should be tried after the Sierpinski's Triangle Activity for comparison purposes.
To build the Sierpinski's Carpet, start with a square with side length 1 unit, completely shaded.
The limiting figure for this process is called the Sierpinski's Carpet.
www.shodor.org /MASTER/interactivate/activities/carpet/what.html   (115 words)

  
 EIMM_C12   (Site not responding. Last check: 2007-11-06)
s in the case of the Sierpinski gasket, fractal patterns can be generated in more than one way.
In the case of the Sierpinski gasket we were able to create it using the SG procedure or by playing the Chaos Game.
Look at method 1 and determine the pattern used to generate the carpet.
www.prenhall.com /divisions/esm/app/ph-la/excursions/html/EIMM_C12.html   (179 words)

  
 Communications Group
The stacked plain carpet element is similar to the Sierpinski element but does not have the pattern etched on the printed circuit substrates.
Similar asymmetries are noted in the E-plane, to those in the patterns of the stacked Sierpinski Carpet antenna.
The measured input return loss of the stacked Sierpinski carpet element with cavity and flange is shown in Figure 6.
postgrad.eee.bham.ac.uk /heetw   (1206 words)

  
 Rug and Carpet: Sierpinski's Carpet   (Site not responding. Last check: 2007-11-06)
This means you have access to the best sierpinski's carpet the world has to offer.
Your sierpinski's carpet is just a point and click away.
While some people are quite content with their carpetting, hardwood floors, or tile, these various types of flooring can be enhanced with all sorts of rugs.
www.rug-and-carpet.com /2005/05/sierpinskis-carpet.php   (198 words)

  
 Mrs. Tate's Fractals WebQuest TeacherWeb Sierpinski Triangle   (Site not responding. Last check: 2007-11-06)
Turn of the century mathematician Waclaw Sierpinski's name was given to several fractal objects, the most famous being his Triangle or Gasket.
Use this Sierpinski fractal applet and select different color combinations as you move from one iteration to the next.
The Sierpinski Gasket Maker at the next site can be used to explore generalizations to the Sierpinski shapes in which you can specify both a movement probability and a rotation.
teacherweb.com /FL/CollierWebQuests/Fractals/wqr3.stm   (322 words)

  
 The Magic Sierpinski Triangle
This design is called Sierpinski's Triangle (or gasket), after the Polish mathematician Waclaw Sierpinski who described some of its interesting properties in 1916.
The large blue triangle consists of three smaller blue triangles, each of which itself consists of three smaller blue triangles, each of which..., a process of subdivision which could, with adequate screen resolution, be seen to continue indefinitely.
Fractals and self-similarity are of considerable interest in their own right, but our interest here is in how to construct Sierpinski's triangle.
serendip.brynmawr.edu /complexity/sierpinski.html   (973 words)

  
 Photo Sierpinski Carpet and More Carpets Sub Categories   (Site not responding. Last check: 2007-11-06)
Photo Sierpinski Carpet - His two brothers, finding him badly burned around the hands and feet, rushed him to hexham general hospital where he admitted to relatives that he had had a lucky escape.
Photo Sierpinski Carpet - By marianne katoppohe stood on the sidewalk in front of the shop and looked at the sign: sale, carpets and rugs.
friday at smith and burstert oriental carpets, 122 southwest blvd.A month ago, the steamy riverfront in new orleans offered michael rogers a much-needed vacation after a year s tour in iraq.
www.carpets617.com /i2_Photo-Sierpinski-Carpet.html   (285 words)

  
 efg's Fractals And Chaos -- Sierpinski Triangle Lab Report
Polish mathematician Waclaw Sierpinski introduced the "Sierpinski Gasket" in 1915.
A Sierpinski Triangle can be formed in a variety of other ways.
At this time an old DOS version of this technique is available in the "Language of Patterns" program, which was originally written for the Maryland Science Center.
www.efg2.com /Lab/FractalsAndChaos/SierpinskiTriangle.htm   (659 words)

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