Movies (Notes) … (a Mosaic Design)

Other methods also exist for describing polygonal tilings. When the tessellation is made of regular polygons, the most common notation is the vertex configuration , which is simply a list of the number of sides of the polygons around a vertex. The square tiling has a vertex configuration of 4. The tiling of regular hexagons is noted 6. Mathematicians use some technical terms when discussing tilings. An edge is the intersection between two bordering tiles; it is often a straight line. A vertex is the point of intersection of three or more bordering tiles. Using these terms, an isogonal or vertex-transitive tiling is a tiling where every vertex point is identical; that is, the arrangement of polygons about each vertex is the same.

The sides of the polygons are not necessarily identical to the edges of the tiles. An edge-to-edge tiling is any polygonal tessellation where adjacent tiles only share one full side, i. In an edge-to-edge tiling, the sides of the polygons and the edges of the tiles are the same. The familiar "brick wall" tiling is not edge-to-edge because the long side of each rectangular brick is shared with two bordering bricks. A normal tiling is a tessellation for which every tile is topologically equivalent to a disk , the intersection of any two tiles is a single connected set or the empty set , and all tiles are uniformly bounded.

This means that a single circumscribing radius and a single inscribing radius can be used for all the tiles in the whole tiling; the condition disallows tiles that are pathologically long or thin. A monohedral tiling is a tessellation in which all tiles are congruent ; it has only one prototile. A particularly interesting type of monohedral tessellation is the spiral monohedral tiling. The first spiral monohedral tiling was discovered by Heinz Voderberg in ; the Voderberg tiling has a unit tile that is a nonconvex enneagon.

Hunt in , is a pentagon tiling using irregular pentagons: An isohedral tiling is a special variation of a monohedral tiling in which all tiles belong to the same transitivity class, that is, all tiles are transforms of the same prototile under the symmetry group of the tiling. A regular tessellation is a highly symmetric , edge-to-edge tiling made up of regular polygons , all of the same shape. There are only three regular tessellations: All three of these tilings are isogonal and monohedral.

A semi-regular or Archimedean tessellation uses more than one type of regular polygon in an isogonal arrangement. There are eight semi-regular tilings or nine if the mirror-image pair of tilings counts as two. Tilings with translational symmetry in two independent directions can be categorized by wallpaper groups , of which 17 exist. Though this is disputed, [33] the variety and sophistication of the Alhambra tilings have surprised modern researchers.

Tilings in 2D with translational symmetry in just one direction can be categorized by the seven frieze groups describing the possible frieze patterns. Penrose tilings , which use two different quadrilateral prototiles, are the best known example of tiles that forcibly create non-periodic patterns. They belong to a general class of aperiodic tilings , which use tiles that cannot tessellate periodically.

The recursive process of substitution tiling is a method of generating aperiodic tilings. One class that can be generated in this way is the rep-tiles ; these tilings have surprising self-replicating properties. Aperiodic tilings, while lacking in translational symmetry , do have symmetries of other types, by infinite repetition of any bounded patch of the tiling and in certain finite groups of rotations or reflections of those patches.

Wang tiles are squares coloured on each edge, and placed so that abutting edges of adjacent tiles have the same colour; hence they are sometimes called Wang dominoes. A suitable set of Wang dominoes can tile the plane, but only aperiodically. This is known because any Turing machine can be represented as a set of Wang dominoes that tile the plane if and only if the Turing machine does not halt. Since the halting problem is undecidable, the problem of deciding whether a Wang domino set can tile the plane is also undecidable.

These can tile the plane either periodically or randomly. Sometimes the colour of a tile is understood as part of the tiling; at other times arbitrary colours may be applied later. When discussing a tiling that is displayed in colours, to avoid ambiguity one needs to specify whether the colours are part of the tiling or just part of its illustration. This affects whether tiles with the same shape but different colours are considered identical, which in turn affects questions of symmetry. The four colour theorem states that for every tessellation of a normal Euclidean plane , with a set of four available colours, each tile can be coloured in one colour such that no tiles of equal colour meet at a curve of positive length.

The colouring guaranteed by the four colour theorem does not generally respect the symmetries of the tessellation. To produce a colouring which does, it is necessary to treat the colours as part of the tessellation. Here, as many as seven colours may be needed, as in the picture at right.

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• Tessellation.

Next to the various tilings by regular polygons , tilings by other polygons have also been studied. Any triangle or quadrilateral even non-convex can be used as a prototile to form a monohedral tessellation, often in more than one way. Copies of an arbitrary quadrilateral can form a tessellation with translational symmetry and 2-fold rotational symmetry with centres at the midpoints of all sides.

For an asymmetric quadrilateral this tiling belongs to wallpaper group p2. As fundamental domain we have the quadrilateral. Equivalently, we can construct a parallelogram subtended by a minimal set of translation vectors, starting from a rotational centre. We can divide this by one diagonal, and take one half a triangle as fundamental domain. Such a triangle has the same area as the quadrilateral and can be constructed from it by cutting and pasting. If only one shape of tile is allowed, tilings exists with convex N -gons for N equal to 3, 4, 5 and 6.

Voronoi or Dirichlet tilings are tessellations where each tile is defined as the set of points closest to one of the points in a discrete set of defining points. Think of geographical regions where each region is defined as all the points closest to a given city or post office. The Delaunay triangulation is a tessellation that is the dual graph of a Voronoi tessellation.

Delaunay triangulations are useful in numerical simulation, in part because among all possible triangulations of the defining points, Delaunay triangulations maximize the minimum of the angles formed by the edges. Tessellation can be extended to three dimensions. Certain polyhedra can be stacked in a regular crystal pattern to fill or tile three-dimensional space, including the cube the only Platonic polyhedron to do so , the rhombic dodecahedron , the truncated octahedron , and triangular, quadrilateral, and hexagonal prisms , among others.

A Schwarz triangle is a spherical triangle that can be used to tile a sphere. Tessellations in three or more dimensions are called honeycombs. In three dimensions there is just one regular honeycomb, which has eight cubes at each polyhedron vertex. Similarly, in three dimensions there is just one quasiregular [c] honeycomb, which has eight tetrahedra and six octahedra at each polyhedron vertex. However, there are many possible semiregular honeycombs in three dimensions. The Schmitt-Conway biprism is a convex polyhedron with the property of tiling space only aperiodically.

It is possible to tessellate in non-Euclidean geometries such as hyperbolic geometry. A uniform tiling in the hyperbolic plane which may be regular, quasiregular or semiregular is an edge-to-edge filling of the hyperbolic plane, with regular polygons as faces ; these are vertex-transitive transitive on its vertices , and isogonal there is an isometry mapping any vertex onto any other. What occurs at the end of this sequence relates to this notion of fragmentation: The mosaic-screen arranges diverse images normally with distinct aesthetic properties: In another paper on 24 , Michael Allen is sensitive to these differences between mosaic-screen and split-screen.

His stimulating account of the history of multi-panel forms spans from medieval paintings to comic books and covers an ampler view of multiple-image techniques. The scholar views the way multiple images are organised in the series as different from screen splitting and describes it as image composition on screen — even if he accepts the inapplicable expression split-screen.

Mosaic (web browser) - Wikipedia

In this way, 24 utilises one the major features of the comic book layout aesthetic to reveal and substantiate narrative and psychological detail developed on other layers of the text. In this passage, Allen is responsive to how the mosaic-screen composes attention — which differs strikingly from the way the split screen divides it. If the split screen draws attention to points of division both along and within the screen edges, the mosaic-screen draws it to the relationships of the detached images set out on a customarily black background. The split screen is routinely used to connect images whereas the mosaic-screen is habitually used to disconnect them.

There are, of course, cases in which the mosaic-screen explores situations that have become usual in the split screen — phone conversations, as evidenced, are regular in 24 —, but here, the space around and in between the frames, more easily conveys degrees of disconnection, prompting the above interpretation. The Thomas Crown Affair However, it is a mistake to think that large gutters are enough to define a mosaic-screen.

The Thomas Crown Affair Norman Jewison, is notable for its use of multiple-frame imagery, split screens as well as mosaic-screens. In an exemplary moment, the film presents two shots on screen. A close-up of Thomas Crown Steve McQueen , a millionaire thief, occupies the whole screen, but is split into six by an added grid.

A medium shot of one of his accomplices in the bank robbery then fills one of the resultant parts. This moment can be fruitfully contrasted with the last instants of the opening credit sequence. Two pictures on the left get smaller: A narrow vertical figure of Vicki is expanded from left to right; the final height is more than three times that of the first pictures. The scale and colour differences contribute to a sense of balance: A moving picture of a man walking in a hallway is inserted and is at variance with the first three still pictures — but it appears at the centre of the screen, prolonging the equilibrium, the inaugural stability of this often tense thriller.

In the first moment, the split screen is used as a means to unevenly fracture a shot and incorporate another. In the initial credits, the mosaic-screen is employed to achieve a vivid sense of adjusted balance. A mosaic is produced from arranged pieces. The use of the mosaic-screen is at times striking — as when the year-old is travelling at the back of an empty city bus, naked, and covered by a torn shower curtain.

Mosaic (web browser)

On the left, there are fragments of the same shot: There is no masking over the shot as in the first example from The Thomas Crown Affair. The pieces were clearly moved away to amplify the feeling of isolation and loneliness. An image of the bus on the road is situated at the bottom right and is considerably bigger than the other three. That alone makes it prominent, but this image is given even more emphasis because it is rotated to the right — a rotation that we follow.

This more dynamic positioning combined with the movement of the bus creates a greater disparity between this image and the stillness of the fragments on the top left. At times, the film combines multiple insets forming a saturated and dispersed image, cubist in its effect — encompassing multiplied viewpoints, simple quadrilateral forms, interlocking planes, and a sense of collage, obviously connected with the idea of mosaic. Billy Gallo sits on a bench right after his release from jail and an image of him in the shower is placed at the centre of the screen. One by one, several images of his recent past fill the screen until the initial shot of the protagonist on a bench disappears under them.

These concise analyses prove that this formal and technical practice exists and has a set of distinctive characteristics. Even so, this is not the same as arguing for the appropriateness of the term, which may be unsuitable to designate such a technique. Craig Knowles recuperates the concept of mosaic as an art form that can be explored in filmmaking. According to him, multiple-imaging in motion pictures is part of a history of decorative and artistic mosaic forms whose origin can be traced back to the Greeks , 9.

For Knowles, mosaic forms maintain a connection with this source: It is not surprising then that he simply gathers modes of presenting several images on screen: Legitimately for his goals, the author not only makes no attempt to distinguish between multiple-image practices, but also mentions the listed techniques as simply creating image mosaics — and hence their effects seems similar and their distinctions become vague. As stated in the description of one of these services, interactive video mosaics4 can display as few as two and as many as twelve video streams.

These video windows can be scaled and the mosaic also includes a channel list and a menu for additional details on selected video streams or television channels. What is fundamental to our discussion is that the variety of information to be displayed begs for an arrangement that is conceptually similar to the mosaic-screen technique: The phosphor screen of television sets is not a surface for projection; it is part of a device that generates the image.

This does not mean that the word is, in itself, problematic. This is an entrenched and comprehensible use of the word. Examining the two words combined leads to other observations. The verb indicates that the split screen emerges from the form and boundaries of the screen; it entails the action of dividing the screen into parts. The noun denotes that the mosaic-screen is arranged over the screen; it identifies a type of composition of images on screen. The foremost evidence that this new term is needed is how the images produced with this technique have observable and significant differences from the ones created employing split-screen imaging.

Behind this assertion is the idea that specific terms can be established and refined — and sometimes established through a process of refinement. As such, the differentiation between the split screen and the mosaic-screen is as critical, and as subtle or apparent, as the one between a matched cut and a jump cut. The clear distinction drawn between split-screen and mosaic-screen in the first sections demonstrated the necessity and usefulness of this new term by showing its descriptive value and practical application.

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One of the advantages of what is proposed here is that it does not require or call for the substitution of one term for another. This is of special significance given that terms become ingrained by their usage — which means that if this essay were proposing such a replacement, even if for a more precise expression, it would encounter resistance, at the least, or indifference, most likely. It has been made clear that split-screen and mosaic-screen are two distinct multi-image techniques and this is the chief reason why we should have two terms to designate them.

The split screen divides the screen into two or more parts.

The mosaic-screen arranges one or more detached images on screen. These two general definitions are open. They do not tell us if the split-screen parts have varying or equal dimensions, or if the mosaic-screen images have similar or different characteristics. Usually, split-screen parts are equivalent and mosaic-images are heterogeneous, but that is not always the case.

If this sounds wrong, consider Mosaic.

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Mosaic is the celebrated graphical "browser" that allows users to travel through the world of electronic information using a point-and-click interface. Mosaic's charming appearance encourages users to load their own documents onto the Net, including color photos, sound bites, video clips, and hypertext "links" to other documents. By following the links - click, and the linked document appears - you can travel through the online world along paths of whim and intuition. Mosaic is not the most direct way to find online information.

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Nor is it the most powerful. It is merely the most pleasurable way, and in the 18 months since it was released, Mosaic has incited a rush of excitement and commercial energy unprecedented in the history of the Net. Mosaic was the web browser that led to the Internet boom of the s. Robert Reid underscores this importance stating, "while still an undergraduate, Marc wrote the Mosaic software Most significantly, their work transformed the appeal of the Web from niche uses in the technical area to mass-market appeal. In particular, these University of Illinois students made two key changes to the Web browser, which hyper-boosted its appeal: Mosaic is not the first web browser for Microsoft Windows; this is Thomas R.

Bruce 's little-known Cello. Other than displaying images embedded in the text rather than in a separate window, Mosaic's original feature set is not greater than of the browsers on which it was modeled, such as ViolaWWW. Reid also refers to Matthew K.

Gray 's website, Internet Statistics: Growth and Usage of the Web and the Internet , which indicates a dramatic leap in web use around the time of Mosaic's introduction. Marc Andreessen's realization of Mosaic, based on the work of Berners-Lee and the hypertext theorists before him, is generally recognized as the beginning of the web as it is now known. Mosaic, the first web browser to win over the Net masses, was released in and made freely accessible to the public.

The adjective phenomenal, so often overused in this industry, is genuinely applicable to the Starting with next to nothing, the rates of the web growth quoted in the press hovering around tens of thousands of percent over ridiculously short periods of time were no real surprise.

Ultimately, web browsers such as Mosaic became the killer applications of the s. Web browsers were the first to bring a graphical interface to search tools the Internet's burgeoning wealth of distributed information services. A mid guide lists Mosaic alongside the traditional, text-oriented information search tools of the time, Archie and Veronica , Gopher , and WAIS [28] but Mosaic quickly subsumed and displaced them all. Joseph Hardin, the director of the NCSA group within which Mosaic was developed, said downloads were up to 50, a month in mid In November , there were twenty-six websites in the world [30] and each one attracted attention.

In its release year of , Mosaic had a What's New page, and about one new link was being added per day.

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This was a time when access to the Internet was expanding rapidly outside its previous domain of academia and large industrial research institutions. Yet it was the availability of Mosaic and Mosaic-derived graphical browsers themselves that drove the explosive growth of the Web to over 10, sites by Aug and millions by A few people noticed that the Web might be better than Gopher. Several million then suddenly noticed that the Web might be better than sex.

Mosaic's popularity as a separate browser began to lessen upon the release of Andreessen's Netscape Navigator in By its user base had almost completely evaporated, being replaced by other web browsers.