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Mandlebulb3D fractal program
View my recent images on Flickriver www.flickriver.com/photos/33235233@N05/
I have just started using this program a couple of days ago, its exciting to try out a new experience
Inside the historic Menger Hotel in San Antonio. The Menger was established in 1859 and sits adjacent to The Alamo.
Tata Steel beschikt over 12 locomotieven van de serie 900. Deze diesellocomotieven zijn gebouwd door General Electric en al meer dan 50 jaar in dienst. Dagelijks rijden de loco's met allerlei treinen over het terrein van Tata, waarbij zoal kalk, vloeibaar ijzer en staalrollen per spoor worden vervoerd. Op 19 april 2017 is loco 909 met een beladen menger/torpedowagen onderweg van Hoogoven 6 naar de Oxystaalfabriek.
In 2017 heeft Bemo Rail de opdracht ontvangen voor het ombouwen van de serie 900 van Tata Steel. De loco's worden compleet gestript en opnieuw opgebouwd en krijgen daarbij onder andere nieuwe motoren, generatoren en een volledig nieuwe kleurstelling. Als alles nog volgens plan verloopt zal de eerste nieuwe locomotief binnen afzienbare tijd in Beverwijk arriveren.
Vlak voordat werd besloten om weer terug richting Nederland te rijden, kwam loc 548 van Eisenbahn und Häfen in de avond van 4 mei nog langs Duisburg Hochfeld met een torpedowagen. De menger, ingeklemd tussen twee rongenwagens, is afkomstig van HKM.
Menger sponge
From Wikipedia, the free encyclopedia
An illustration of M4, the sponge after four iterations of the construction process
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge)[1][2][3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.[4][5]
Construction
The construction of a Menger sponge can be described as follows:
Begin with a cube.
Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes.
Remove the smaller cube in the middle of each face, and remove the smaller cube in the center of the more giant cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).
Repeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration gives a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration
Properties
Hexagonal cross-section of a level-4 Menger sponge. (Part of a series of cuts perpendicular to the space diagonal.)
The n nth stage of the Menger sponge, M n M_{n}, is made up of 20 n {\displaystyle 20^{n}} smaller cubes, each with a side length of (1/3)n. The total volume of M n M_{n} is thus ( 20 27 ) n {\textstyle \left({\frac {20}{27}}\right)^{n}}. The total surface area of M n M_{n} is given by the expression 2 ( 20 / 9 ) n + 4 ( 8 / 9 ) n {\displaystyle 2(20/9)^{n}+4(8/9)^{n}}.[6][7] Therefore, the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues so that the limit is neither a solid nor a surface; it has a topological dimension of 1 and is accordingly identified as a curve.
Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry.[8] The number of these hexagrams, in descending size, is given by a n = 9 a n − 1 − 12 a n − 2 {\displaystyle a_{n}=9a_{n-1}-12a_{n-2}}, with a 0 = 1 , a 1 = 6 {\displaystyle a_{0}=1,\ a_{1}=6}.[9]
The sponge's Hausdorff dimension is log 20/log 3 ≅ 2.727. The Lebesgue covering dimension of the Menger sponge is one, the same as any curve. Menger showed, in the 1926 construction, that the sponge is a universal curve, in that every curve is homeomorphic to a subset of the Menger sponge, where a curve means any compact metric space of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways. Similarly, the Sierpinski carpet is a universal curve for all curves that can be drawn on the two-dimensional plane. The Menger sponge constructed in three dimensions extends this idea to graphs that are not planar and might be embedded in any number of dimensions.
The Menger sponge is a closed set; since it is also bounded, the Heine–Borel theorem implies that it is compact. It has Lebesgue measure 0. Because it contains continuous paths, it is an uncountable set.
Experiments also showed that cubes with a Menger sponge structure could dissipate shocks five times better for the same material than cubes without any pores.[10]
(As if 052309 this image has been view 760 times and has been added to Mrbill's Geriatric Ward to determine if any of the members can figure out why this particular image has been viewed that many times.)
... IN SEARCH OF A HERO. The cloudiness of my memory amazes me. I remebered our first World War II hero, Colin Kelly. To my credit, when I typed in his name to Yahoo search, I did spell it correctly. I remembered that Colin Kelly had dived his PBY seaplane into a Japanese submarine. I was 14 years old at the time and not a daily reader of the news. This from Wikipedia:
Colin Purdie Kelly, Jr. (July 11, 1915 – December 10, 1941). Born in Madison, Florida, he was a World War II B-17 Flying Fortress pilot who flew bombing runs against the Japanese navy in the first days after the Pearl Harbor attack. He is remembered as a war hero for sacrificing his own life to save his crew when his plane became the first American B-17 to be shot down in combat. Colin Kelly has been called the first American hero of the Second World War.
On December 10, 1941, Kelly's plane lifted off from Clark Field in the Philippines. During its bombing run, Kelly's bomber hit the Japanese cruiser Ashigara. On its return flight the bomber came under attack by Zeros, one of which was piloted by famed Japanese flying ace Saburo Sakai. Kelly stayed at the controls of the badly damaged aircraft so that the surviving crew members could bail out. Just after the last crew member escaped the plane exploded. Early reports misidentified the Ashigara as the battleship Haruna, and also mistakenly reported that he had crashed his plane into the smokestack of the Haruna, becoming the first Suicide pilot of the war.
For his extraordinary heroism and selfless bravery, Kelly was posthumously awarded the Distinguished Service Cross.
Aviation artist Robert Taylor has painted a painting entitled The Legend of Colin Kelly. (My illustration is a corruption of that painting.)
In World War II the United States liberty ship SS Colin P. Kelly, Jr. was named in his honor.
I also remember during those first months of World War II, the city of Corpus Christi renamed 13th Street, Brownlee Blvd. in honor of the first or near first Corpus Christi service man to die in battle. I was a member of Boy Scout Troop2, sponsored by the First Presbyterian Church of Corpus Christi, Texas. Since Brownlee had been a member of that troop, we were present at the dedication service, led by the mayor, just outside Menger Elementary School on Brownlee Blvd. Now I'll have to see if I can find Brownlee's first name on the internet and check to see if my Email buddy, James Ross Underwood, who was also in Troop 2 remembers that short ceremony.
2020 - © This photograph is copyrighted. Under no circumstances can it be reproduced or used in any form without the prior written consent and permission of the photographer.
Voor het spoorvervoer binnen Tata Steel IJmuiden beschikt het bedrijf over 17 eigen locomotieven. 5 van de serie 800 (de fluisterloco's) en 12 van de serie 900.
Voor het transport van vloeibaar ijzer tussen de hoogovens en de oxystaalfabriek rijden de hele dag de 900 loco's met torpedowagens heen en weer. De immense wagens hebben beladen een gewicht van max 800 ton, en dat onberemd.
Aan het eind van de ochtend rijdt de 902 met 2 lege wagens van de Oxystaalfabriek naar de Hoogovens, alwaar ze opnieuw beladen kunnen worden met vloeibaar ijzer.
San Antonio, Texas
'The San Antonio Japanese Tea Garden, or Sunken Gardens in Brackenridge Park opened in an abandoned limestone rock quarry in the early 20th century. It was known also as Chinese Tea Gardens, Chinese Tea Garden Gate, Chinese Sunken Garden Gate and is listed on the U.S. National Register of Historic Places. It was developed on land donated to the city in 1899 by George Washington Brackenridge, president of the San Antonio Water Works Company. The ground was first broken around 1840 by German masons, who used the readily accessible limestone to supply the construction market. Many San Antonio buildings, including the Menger Hotel, were built with the stone from this quarry on the Rock Quarry Road.' (Wikipedia)
A development on the Egyptian fractal theme. Managed to find a transcript of the Rosetta stone, and used it as a heightmap over a sphere and a plane, added a Menger hypercube, texture and lights, et voila!
The Rosetta Stone was the original key to the decipherment of hieroglyphics. It was a damaged stone (much of the top is missing), found by Napoleon's invading army, at Rosetta (apparently French for Rashid) in northern Egypt, in 1799. It was captured by the British while still in Egypt, and is now in the British Museum. It is a stela (or stele, a stone with writing carved on it) with the same message (a decree from Ptolemy V) repeated three times, in hieroglyphics (Late Egyptian), in Demotic (another version of Egyptian), and in Greek. The first 26 or so lines are missing from the hieroglyphic part. The Rosetta Stone enabled Champollion and others to finally make progress deciphering hieroglyphics.
The Sphere has the cartouche of the pharaoh Ptolemy on the front, further down the script the cartouche is repeated, but misspelt. It can be seen in the right hand corner of the image. The second from last glyph is missing! I wonder how long the scribe lived after spelling the pharaohs name wrong?!!!
info courtesy www.jimloy.com/egypt/rosetta.htm
Another fractal to make Explore! Thanks to everyone! =]
Excerpt from en.wikipedia.org/wiki/Jagiellonian_University:
The Jagiellonian University (Polish: Uniwersytet Jagielloński, UJ) is a public research university in Kraków, Poland. Founded in 1364 by King Casimir III the Great, it is the oldest university in Poland and the 13th oldest university in continuous operation in the world. It is regarded as Poland's most prestigious academic institution. The university has been viewed as a vanguard of Polish culture as well as a significant contributor to the intellectual heritage of Europe.
The campus of the Jagiellonian University is centrally located within the city of Kraków. The university consists of thirteen main faculties, in addition to three faculties composing the Collegium Medicum. It employs roughly 4,000 academics and provides education to more than 35,000 students who study in 166 fields. The main language of instruction is Polish, although around 30 degrees are offered in English and some in German. The university library is among the largest of its kind and houses a number of medieval manuscripts, including the landmark De Revolutionibus by alumnus Nicolaus Copernicus.
In addition to Copernicus, the university's notable alumni include heads of state King John III Sobieski, Pope John Paul II, and Andrzej Duda; Polish prime ministers Beata Szydło and Józef Cyrankiewicz; renowned cultural figures Jan Kochanowski, Stanisław Lem, and Krzysztof Penderecki; and leading intellectuals and researchers such as Hugo Kołłątaj, Bronisław Malinowski, Carl Menger, Leo Sternbach, and Norman Davies. Four Nobel laureates have been affiliated with the university, all in literature: Ivo Andrić and Wisława Szymborska, who studied there, and Czesław Miłosz and Olga Tokarczuk, who taught there. Faculty and graduates of the university have been elected to the Polish Academy of Arts and Sciences, the Royal Society, the British Academy, the American Academy of Arts and Sciences, and other honorary societies.
Created with Mandelbulb 3D V.199.27 - than traced with Bulbtracer 2 and rendered with Cinema 4D
PS: its my first Trace, i hope, its ok .
Menger sponge
From Wikipedia, the free encyclopedia
An illustration of M4, the sponge after four iterations of the construction process
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge)[1][2][3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.[4][5]
Construction
The construction of a Menger sponge can be described as follows:
Begin with a cube.
Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes.
Remove the smaller cube in the middle of each face, and remove the smaller cube in the center of the more giant cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).
Repeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration gives a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration
Properties
Hexagonal cross-section of a level-4 Menger sponge. (Part of a series of cuts perpendicular to the space diagonal.)
The n nth stage of the Menger sponge, M n M_{n}, is made up of 20 n {\displaystyle 20^{n}} smaller cubes, each with a side length of (1/3)n. The total volume of M n M_{n} is thus ( 20 27 ) n {\textstyle \left({\frac {20}{27}}\right)^{n}}. The total surface area of M n M_{n} is given by the expression 2 ( 20 / 9 ) n + 4 ( 8 / 9 ) n {\displaystyle 2(20/9)^{n}+4(8/9)^{n}}.[6][7] Therefore, the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues so that the limit is neither a solid nor a surface; it has a topological dimension of 1 and is accordingly identified as a curve.
Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry.[8] The number of these hexagrams, in descending size, is given by a n = 9 a n − 1 − 12 a n − 2 {\displaystyle a_{n}=9a_{n-1}-12a_{n-2}}, with a 0 = 1 , a 1 = 6 {\displaystyle a_{0}=1,\ a_{1}=6}.[9]
The sponge's Hausdorff dimension is log 20/log 3 ≅ 2.727. The Lebesgue covering dimension of the Menger sponge is one, the same as any curve. Menger showed, in the 1926 construction, that the sponge is a universal curve, in that every curve is homeomorphic to a subset of the Menger sponge, where a curve means any compact metric space of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways. Similarly, the Sierpinski carpet is a universal curve for all curves that can be drawn on the two-dimensional plane. The Menger sponge constructed in three dimensions extends this idea to graphs that are not planar and might be embedded in any number of dimensions.
The Menger sponge is a closed set; since it is also bounded, the Heine–Borel theorem implies that it is compact. It has Lebesgue measure 0. Because it contains continuous paths, it is an uncountable set.
Experiments also showed that cubes with a Menger sponge structure could dissipate shocks five times better for the same material than cubes without any pores.[10]
We made her the final stop on our tour of the Missions of San Antonio World Heritage Site self guided tour; despite the fact she was right next door to our stay in The Menger Hotel (oldest continuously operating hotel west of the Mississippi). She is a place so revered that even modern construction is forbade to let a building shadow fall across her. Thirty Tennesseeans, including Davy Crockett, alongside folks from many other states and countries laid down their lives rather than give up. It is first and foremost a Church; rest, sanctuary, and, communion.
A bisected level 4 Menger Sponge.
I added a tag "Optical Illusion" because if you stare at it long enough, she is either about to escape through a hole in the floor of the cube above, or to on top of an orange flange. The trick is to visualize the edge to her right as an external or internal corner.
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This image and its name are protected under copyright laws.
All their rights are reserved to my own and unique property.
Any download, copy, duplication, edition, modification,
printing, or resale is stricly prohibited.
*******************************************************************************
What I like about Texas!... The Alamo, The Menger, Riverwalk and Mi Tierra...Just like a Gary P. Nunn song.
You ask me what I like about Texas...
It's driving El Camino Real into San Antone
It's the Riverwalk and Mi Tierra
Jammin' out with Bongo Joe
It's stories of the Menger Hotel and the Alamo!
(You remember the Alamo!)
Not then, not now, not ever (Truus Menger, 1982)
Double Exposure,
Agfa Paratic
Osnabrück Hauptbahnhof,
16/05/2010
I haven't uploaded in a while, so here is an image from my queue.
It's another level 1 Menger Sponge colored in a special way. This is the first time I've managed to color any origami with a gradient that was neither horizontal nor vertical.
As usual, there are 144 units in the construct. However, the number of individual units of each color was difficult for me to predict and didn't follow any interesting pattern (so much for my Pascal Triangle theory!) I miscalculated the number of colors needed to color the unit, so I ended up filling in the missing colors with pink and white. I think it turned out okay.
A level 1 Menger Sponge (a kind of 3D fractal) made out of Tomoko Fuse's open frame units. It's easy to tell how many units are required: (8 outside squares + 4 inside squares) per face * 6 faces = 72 squares total; each square has 4 edges giving 72 * 4 = 288 edges total, and then divide that by 2 since each edge belongs to two squares. It turns out that an Nth-level Menger Sponge requires 12^(N+1) edges using this formula. Edit: Don't rely on that simplistic formula; it was incorrect.)
Please forgive the superimposed text. This picture originally went into a brochure that Addie_Goodvibes and I put together, and I don't have the original object on me anymore. It's probably crinkled because something was resting on it at some point....
Menger sponge
From Wikipedia, the free encyclopedia
An illustration of M4, the sponge after four iterations of the construction process
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge)[1][2][3] is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.[4][5]
Construction
The construction of a Menger sponge can be described as follows:
Begin with a cube.
Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes.
Remove the smaller cube in the middle of each face, and remove the smaller cube in the center of the more giant cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).
Repeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration gives a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration
Properties
Hexagonal cross-section of a level-4 Menger sponge. (Part of a series of cuts perpendicular to the space diagonal.)
The n nth stage of the Menger sponge, M n M_{n}, is made up of 20 n {\displaystyle 20^{n}} smaller cubes, each with a side length of (1/3)n. The total volume of M n M_{n} is thus ( 20 27 ) n {\textstyle \left({\frac {20}{27}}\right)^{n}}. The total surface area of M n M_{n} is given by the expression 2 ( 20 / 9 ) n + 4 ( 8 / 9 ) n {\displaystyle 2(20/9)^{n}+4(8/9)^{n}}.[6][7] Therefore, the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues so that the limit is neither a solid nor a surface; it has a topological dimension of 1 and is accordingly identified as a curve.
Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry.[8] The number of these hexagrams, in descending size, is given by a n = 9 a n − 1 − 12 a n − 2 {\displaystyle a_{n}=9a_{n-1}-12a_{n-2}}, with a 0 = 1 , a 1 = 6 {\displaystyle a_{0}=1,\ a_{1}=6}.[9]
The sponge's Hausdorff dimension is log 20/log 3 ≅ 2.727. The Lebesgue covering dimension of the Menger sponge is one, the same as any curve. Menger showed, in the 1926 construction, that the sponge is a universal curve, in that every curve is homeomorphic to a subset of the Menger sponge, where a curve means any compact metric space of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways. Similarly, the Sierpinski carpet is a universal curve for all curves that can be drawn on the two-dimensional plane. The Menger sponge constructed in three dimensions extends this idea to graphs that are not planar and might be embedded in any number of dimensions.
The Menger sponge is a closed set; since it is also bounded, the Heine–Borel theorem implies that it is compact. It has Lebesgue measure 0. Because it contains continuous paths, it is an uncountable set.
Experiments also showed that cubes with a Menger sponge structure could dissipate shocks five times better for the same material than cubes without any pores.[10]
Super-wide POV inside a Menger Sponge.
Copyright © 2011 by Craig Paup. All rights reserved.
Any use, printed or digital, in whole or edited, requires my written permission.
*******************************************************************************
This image and its name are protected under copyright laws.
All their rights are reserved to my own and unique property.
Any download, copy, duplication, edition, modification,
printing, or resale is stricly prohibited.
*******************************************************************************
A River Landscape
Artist:
Asher Brown Durand
Date:
1858
Location:
de Young
Gallery 26
Century:
19th Century AD
Media:
Oil On Canvas
Dimensions:
32 x 48 in. (81.3 x 121.9 cm)
Department:
American Painting
Object Type:
Painting
Country:
United States
Continent:
North America
Provenance:
Possibly Lewis M. Rutherford (1816 1892), New York, or L. R. Menger, or Benjamin N. Huntington (ca. 1816 1882), Rome, N.Y., 1858
[Harvey Additon, Boston, ca. 1910]
Winthrop Coffin (ca.. 1863 1938), Brookline, Mass., ca. 1910-1938
Richard S. Halfyard (1901 1988) and Eliza Halfyard (1906 1984), Belmont, Mass., ca. 1938
[Vose Galleries, Boston, 1971—1972]
John D. Rockefeller 3rd and Blanchette Hooker Rockefeller,
New York, 1972—1993
FAMSF, 1993.35.8
Accession Number:
1993.35.8
Acquisition Date:
1993-06-10
Credit Line:
Gift of Mr. and Mrs. John D. Rockefeller 3rd
Exhibition History:
Possibly New York, National Academy of Design, Thirty third Annual Exhibition, 1858, exh. no. 492 (Landscape, lent by L. M. Rutherford) or exh. no. 585 (In New Hampshire, lent by L. R. Menger)
San Francisco 1976, exh. no. 36
Tokyo 1982, exh. no. 27