Squame spiral tessellation

 

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Squame modular tiling creation metod

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Squame Spiral Tessellation

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Definition: A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. A regular tessellation means a tessellation made up of congruent regular polygons. (Regular means that the sides of the polygon are all the same length. Congruent means that the polygons that you put together are all the same size and shape.)

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Squame Spiral Tessellation Inspired by the modular work of M.C.Esher, in 1996 Squamificio discovered a geometric solution that was called Squame. Squame are able to some properties not before seen in geometry.

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Squame modular shapes can do the tessellation of surfaces in all the classical periodic way: by going straight in line, alternate, rotated, mirrored and so on... straight alternate rotated rotated alternate

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The great innovation of Squame is the ability to tessellate not just in one directional way, but also by creating curves (radial tiling). And both modes can be combined together. Concentric Circles Tessellation Curves and Straight Tesellation

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The most beautiful way Squame can tessellate the plane in a non periodical fashion is doing Spirals. Squame Perfect Single Spiral

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No longer limited to old mathematical methods, with Squame, many different spirals compositions are possible. 2 Centers Spiral

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3 Centers Spiral 4 Centers Spiral

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Squame can generate single, double, triple, N centered spirals, depending of the shape and the angle of the module utilized and the effect desired. By combining the differents tecnical possibilities of Squame we can discover new ways to create non periodic tessellation. Voderberg Variation

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Double Voderberg Ibrid Spirals

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How to Generate Squame To generate a Squame module the first thing to do is decide for an angle to apply. Let's say for instance that Alpha would be 30°. Now draw a line: it is a side for your module. Draw a second line of the same length but rotated of Alpha degrees: Keep drawing lines, always rotating by Alpha degrees, until you reach the total limit of 180°.

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Each step you have just drawed it is a pattern that can be replicated by simple translation. Translate each pattern over the Tangent of Alpha/2 (this is the Patented Formula to generate Squame) until vertex coincide. Continue replicating all around and you will obtain a perfect tessellation for each pattern.

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You have just generated 6 different Squame modules of the 30° Family. Right now they are standing in their simplest configuration: the Linear Tessellation, but they are all able to curve by 30° (clockwise and counterclockwise) and keep tiling:

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