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Topic: Hypercube

In the News (Sat 18 May 13)

 Tesseract - Wikipedia, the free encyclopedia In geometry, the tesseract, or hypercube, is a regular convex polychoron with eight cubical cells. In that book she uses the tesseract as a portal, a doorway which you can pass through and emerge far away from the starting point, as if the two distant points were brought together at one intersection (at the tesseract doorway) by the folding of space, enabling near-instantaneous transportation. Hypercubes and all kinds of multi-dimensional space and structures star prominently in many books by Rudy Rucker. en.wikipedia.org /wiki/Hypercube   (1292 words)

 Cube 2: Hypercube A hypercube, or "tesseract" is the four dimensional equivalent of a cube - and an entirely theoretical construct. Hypercube drops hints like it was leaving a trail of crumbs. Hypercube also suffers from weak and sometimes inconsistent characterizations, as well as the occasional head scratching plot twists (one player appears briefly at the film's opening, and shows up toward the end just to be killed without pretense). www.scifidimensions.com /Apr03/hypercube.htm   (497 words)

 Magic hypercube - Wikipedia, the free encyclopedia In mathematics, a magic hypercube is the k-dimensional generalization of magic squares, magic cubes and magic tesseracts, that is, a number of integers arranged in an n x n x n x... If, in addition, the numbers on every cross section diagonal also sum up to the hypercube's magic number, the hypercube is called a perfect magic hypercube; otherwise, it is called a semiperfect magic hypercube. Five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. en.wikipedia.org /wiki/Magic_hypercube   (236 words)

 Typical hypercube geometry   (Site not responding. Last check: 2007-11-06) Hypercubes, also referred to as n-cubes, have been utilized in parallel machines for many years and have been available with a thousand, or more, CPUs. Hydra, the front-end node, was not part of the hypercube and served the function of being the user interface to the cluster. At this point, the hypercube was still not stable, but had to suffice for the remainder of the project as time grew short. www.pcs.cnu.edu /~ksomervi/project/node7.html   (526 words)

 Math 53 Orthographic Views of the Sliced Hypercube (Spring 1999) This movie shows the orthographic view of a hypercube looking directly at a corner of the hypercube (i.e., along its long diagonal) while the hypercube is being sliced parallel to one of its cubical faces. Each vertex of the hypercube is a member of four cubes, so at each endpoint of the initial line segment there is one additional cube; the triangular faces come from these cubes are they are sliced corner first. This corner of the hypercube also appears to be at the center of the projection; since we are looking along the long diagonal, both the closest and farthest points on the hypercube are at the same location in the projection. www.math.union.edu /~dpvc/courses/1998-99/MTH053-SP99/notes/hcube-slices/welcome.html   (936 words)

 [No title] hypercubes are derivable from a single one, denoted by this author as the "Grand-Parential Hypercube". hypercube or vice versa any positon in the hypercube to the hypercube corner. A hypercube derived from a "Grand-Parential Hypercube" by a home.wanadoo.nl /aaledewinkel/Encyclopedia/i/Isomorphisms.html   (1517 words)

 Hypercube   (Site not responding. Last check: 2007-11-06) A friend of mine was reading a book about the fourth dimension and was having a hard time visualizing hypercubes, so I wrote a program so he could play with a hypercube interactively. For a 4D rotation, the 3D vector described by the dragging of the mouse in the plane of the screen combined with the 4D unit vector (0 0 0 1) specify two basis vectors of a four-dimensional plane of rotation. The transparent walls of the hypercube are drawn in such a way that they become slightly less transparent as they are angled edge-on to the camera. www.traipse.com /hypercube   (377 words)

 Hypercube   (Site not responding. Last check: 2007-11-06) When projected down to three dimensions, its projection is a rhombic dodecahedron, with 12 of the hypercube's 24 faces projected into the interior, and 12 forming the surface. A hypercube in 5 dimensions has 32 vertices, 80 edges, 80 square faces, 40 cubic faces, and 10 (4-dimensional) hypercubic faces which form its boundary. When projected down to three dimensions, its projection is a rhombic icosahedron, with 60 of the hypercube's 80 faces projected into the interior, and 20 forming the surface. gregegan.customer.netspace.net.au /APPLETS/29/29.html   (133 words)

 hypercube   (Site not responding. Last check: 2007-11-06) A single (2^0 = 1) point (or "node") can be considered as a zero dimensional cube, two (2^1) nodes joined by a line (or "edge") are a one dimensional cube, four (2^2) nodes arranged in a square are a two dimensional cube and eight (2^3) nodes are an ordinary three dimensional cube. Continuing this geometric progression, the first hypercube has 2^4 = 16 nodes and is a four dimensional shape (a "four-cube") and an N dimensional cube has 2^N nodes (an "N-cube"). The fact that the number of directly connected, "nearest neighbour", nodes increases with the total size of the network is also highly desirable for a parallel computer. www.linuxguruz.com /foldoc/foldoc.php?hypercube   (275 words)

 Hyperspace structures   (Site not responding. Last check: 2007-11-06) A hypercube is a 4 dimensional analogue of the cube. Details of the construction of this object are given, along with movies of a spinning hypercube. By inserting new vertices into the edges and faces of a hypercube, it may be ``inflated'' to give an approximation to the hypersphere. www.lboro.ac.uk /departments/ma/gallery/hyper   (89 words)

 The Hypercube Project IMSAI The Hypercube was advertised as a four dimensional arrangement of dual 8080 processor "nodes" configured in 2x2x2x2, 3x3x3x3, and 4x4x4x4 arrays, with each node capable of communicating, via shared memory, with 8 adjacent nodes. The advertised price of these three offerings was \$80,000 for the Hypercube II, \$400,000 for the Hypercube III (about 1/10th the cost of an IBM 370-168), and \$1,280,000 for the Hypercube IV which was to be released in the second quarter of 1976. The Hypercube was announced in one or a couple press releases, around the same time as the 108. www.imsai.net /history/imsai_history/hypercube_project.htm   (370 words)

 Fourth Dimension   (Site not responding. Last check: 2007-11-06) The Fourth Dimension is portrayed geometrically by fractals and by the Hypercube. The Hypercube is the symbol used in mathematics to try and represent the fourth dimension in two dimensions (a drawing on a piece of paper - a plane). From the center of the Hypercube through its 8 diagonals the Hypercube is related to everything in the Universe. www.fractalwisdom.com /FractalWisdom/fourth.html   (311 words)

 [No title]   (Site not responding. Last check: 2007-11-06) This article deals with the hypercube in general, each n-Point contains a number however no magic condition is imposed yet on the hypercube yet The latin hypercube is generally seen as a component of an hypercube Whether or not the resulting hypercube is magic depends on the given values home.wanadoo.nl /aaledewinkel/Encyclopedia/h/Hypercube.html   (590 words)

 [No title] The binary representation of nodes in a hypercube of dimension k has k bits.(the exception is the singular case of hypercube with k=0). For example, for hypercube with k=3, a bit-position ordered shortest path between nodes 1 (001) and 6 (110) is 1 (001),0(000),2 (010) and 6 (110). Each input set has the dimensionality of a hypercube (the dimension of the hypercube is in the range of 0 up to 20) a source and a destination node (integer numbers in decimal base). icpc.baylor.edu /past/icpc2002/Regionals/CAmerica01/problem5.doc   (636 words)

 The Hypercube The above colored drawing is a 2 dimensional depiction of a hypercube. These are 3d looking 2d drawings of hypercubes. Beginning at the first section, and going to the last, that is what you would get if you were to cut a hypercube into consecutive 3d slices. www.geocities.com /CapeCanaveral/7997/hypercube.html   (181 words)

 Visualizing 4D Hypercube Data By Mapping Onto a 3D Tesseract The data is in a hypercube, the 4-D generalization of a 3-D cube. If they said you generated a hypercube by moving a cube in a perpendicular direction, they would tell you there is no such direction. They could show us an unfolded hypercube (Figure 4), and tell us that these eight cubes can be folded up into a cube, with each cube rotating about a square it borders on. www.well.com /~abs/SIGGRAPH96/4Dtess.html   (1813 words)

 The Tesseract - a 4-dimensional cube Hypercube is a multidimensional analogue of a 3-dimensional cube in that each coordinate of a point in a hypercube is restricted to the same 1-dimensional (line) segment. In anticipation of MAM 2000, a remark by A. Wrote he, "Dimensions seem to creep up in everywhere as HYPERCUBE is written." Dewdney was referring to matrices (2-dimensional objects) and vectors (1-dimensional objects) that are part of any modern computer language. www.cut-the-knot.org /ctk/Tesseract.shtml   (1271 words)

 Hypercube   (Site not responding. Last check: 2007-11-06) Hypercube is a game developer based in Perth, Western Australia. The company was formed early in 2002, with a view to developing better games for handheld consoles, and in particular the Nintendo Gameboy Advance. By taking old-school ideas, and new 3D technologies and retro-fitting them to the smaller format of a handheld console, they plan to create a range of unique GBA games that will look, sound, and play at a quality rarely seen on handheld platforms. www.hypercube.com.au   (112 words)

 Ziggy's Video Realm: Geraint Wyn Davies in Cube 2: Hypercube (2003)   (Site not responding. Last check: 2007-11-06) Cube 2: Hypercube is, in respect to its characters, a carbon copy of the first film, with a far less interesting script surrounding them, and when it is all said and done, the ending will simply leave the audience feeling very cheated, which is a shame, as the first five minutes start out wonderfully. This new cube, or hypercube, is similar to the last in appearance only, as it is a much more complex structure. For those who are interested, the principal of a “hypercube” is very real and is perhaps the only interesting note that can be mentioned about this movie at all. www.reelcriticism.com /ziggyrealm/reviews/cube2.html   (1178 words)

 Cube 2: Hypercube plot summary When she found out they were putting people into the Cube she had tried to blow the whistle, but they chased her and she escaped inside the Cube (the one place they wouldn't dare go). She looks at the watch and realises the number she has seen allover the place including the dead scientists body is the time at which the Hypercube will collapse. She takes Sashas tag as the Hypercube collapses in on itself and then jumps through a portal into fl space. www.ruinedendings.com /film3161plot   (1257 words)

 CM Article in DesignIssues These chips were to be wired together in a network having the shape of a 12-dimensional hypercube. A 5- D hypercube is a square of cubes: This is the structure used in the CM-2, a cube with 2 to the power 12 corners, or 4,096 chips, each connected to 12 other chips, each connection being one dimension of the cube. mission.base.com /tamiko/theory/cm_txts/di-ch2.html   (555 words)

 Cube 2: Hypercube - Twice the suckage   (Site not responding. Last check: 2007-11-06) A hypercube is a mental experiment of what a four dimensional cube might look like. To someone who lives in a two-dimensional universe, the concept of a cube is alien, but a truly inspired 2D person might be able to conceive of this cube that he could never truly see. One of the almost plausible features given to the hypercube is that each room may be oriented differently. www.highprogrammer.com /~chaos/alan/rants/reviews/movies/cube2.html   (1712 words)

 HyperCube This includes the static and dynamic display of the image cube and the generation of spectral classifications using both imagery and spectral libraries. HyperCube will run with only 8 MB but some functions may have to be broken into successive operations. The Windows version (HyperCube.zip, HyperCube) runs on the Windows 95 through XP operating systems. www.tec.army.mil /Hypercube/index.html   (585 words)

 Hypercube This is a sketch I created many years ago to attempt to explain to my friends how a multidimensional object can be visualized in two-space; or what it means to "draw a picture" of "a hypercube" (a 4-dimensional object). Drag point 4 far away, so that its vector becomes very long, and you can see that a hypercube is just two (three-dimensional) cubes, with each vertex connected by a new (green) dimension. The three-dimensional cube is just two squares connected by a new (blue) dimension, and so on. mathforum.org /dynamic/java_gsp/hypercube.html   (657 words)

 Hypercube The hypercube is the cube with four dimensions. The hypercube has 16 corners (derived from 2 cubes) and 32 edges (2 cubes and joining lines). If you "build" a hypercube, you have to stick the remaining 34 squares in pairs. www.mathematische-basteleien.de /hypercube.htm   (650 words)

 Cube 2: Hypercube   (Site not responding. Last check: 2007-11-06) But as the group soon discovers, danger is still present, in the form of colliding realities, future rooms moving into present rooms, and the aptly-named "razorsphere," just a few obstacles standing between the dwindling group of survivors and figuring exactly what in the hell is going on. Paley" into one of those hyper-speed rooms, would ya?) and, what is definitely a big no-no that doesn't come off as bad as expected, tries to delve into the mystery of what the cube is, who created it, and what it's all about. In the case of Cube 2: Hypercube, it's hip to be square. www.ajhakari.com /c/cube2hypercube.html   (848 words)

 FIGS424-Sort a FIGS image-mode hypercube into wavelength order   (Site not responding. Last check: 2007-11-06) Re-orders a raw FIGS image-mode data hypercube so that the spectral dimension is in ascending order of wavelength, instead of in the order as read by the data acquisition system. F I G S 4 2 4 Given a FIGS image-mode data hypercubecube as produced by the FIGS data acquisition system, processes it to produce a hypercube in which the data have been sorted into wavelength order in accordance with the wavelength parameters included in the hypercube. The data is only re-ordered in the first dimension of the hypercube. star-www.rl.ac.uk /star/dvi/sun86.htx/node392.html   (310 words)

 hypercube   (Site not responding. Last check: 2007-11-06) A hypercube is the logical progression of line, square, cube, hypercube. Who's Tardis is a hypercube, and the Starship Enterprise has warp drive that travels in the fourth physical dimension. This hypercube has one of its side MUCH larger than the others, which is why it seems to increase and decrease in size. atoys.com /hcube.html   (841 words)

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