Within the confines of my limited research, it seems that geometric designs in Islamic art hold no specific religious significance (I expect this is a highly controversial statement.) and instead provide an opportunity for craftsmen to demonstrate the skill and subtlety of their workmanship, and to dazzle and intrigue the viewer with their complexity. Well, it turns out that this specific pattern:Īppears originally in Islamic / Arabic / Moorish art. However, this statement was pure speculation based on the appearance of similar patterns in Chinese art, also using the p31m wallpaper tiling method, this one below for example. Previously I'd said, (I believe the pattern is pretty old and of Chinese origin.). Additional notes on the origin of this pattern. I know that this doesn't help too much in understanding less rigid tessellation designs, such as Escher's reptiles, which I assume MCE made intuitively (I read that he wasn't a mathematician, which I was surprised by.)Īnyway, I hope this question isn't too sprawling, and thank you for looking. How to construct the shape unit mathematically.How to calculate the relative positions of each shape to build the grid programmatically.There appears to be a equilateral triangle which contains the key dimensions, and of course the regular hexagon is important, since this essentially forms 2 interwoven hexagonal grids.īeyond this I'm unable to express mathematically what is going on. Here's some examples of patterns I've worked up.īecause I don't really understand the math, I've had to create the basic unit shape by hand, I can see the 60/120 degree angles well enough, but I really want to figure out the proportions of the shape, which appear (from just looking) to be tightly interrelated.Ī few observations I've made during this process (aside from it being a bit more tricky than I first imagined.) In my spare time, I'm playing a lot with a series of patterns which use a hexagonal grid, and a tessellating design I saw on a chair in my dentist's surgery. Escher.Tessellation is fascinating to me, and I've always been amazed by the drawings of M.C.Escher, particularly interesting to me, is how he would've gone about calculating tessellating shapes. Tessellations figure prominently throughout art and architecture from various time periods throughout history, from the intricate mosaics of Ancient Rome, to the contemporary designs of M.C. As you can probably guess, there are an infinite number of figures that form irregular tessellations! Meanwhile, irregular tessellations consist of figures that aren't composed of regular polygons that interlock without gaps or overlaps.Only eight combinations of regular polygons create semi-regular tessellations. Semi-regular tessellations are made from multiple regular polygons.Regular tessellations are composed of identically sized and shaped regular polygons.There are three different types of tessellations ( source): but only if you view the triangular gaps between the circles as shapes. While they can't tessellate on their own, they can be part of a tessellation. Circles can only tile the plane if the inward curves balance the outward curves, filling in all the gaps. What about circles? Circles are a type of oval-a convex, curved shape with no corners. Only three regular polygons(shapes with all sides and angles equal) can form a tessellation by themselves- triangles, squares, and hexagons. In a tessellation, whenever two or more polygons meet at a point (or vertex), the internal angles must add up to 360°. While any polygon (a two-dimensional shape with any number of straight sides) can be part of a tessellation, not every polygon can tessellate by themselves! Furthermore, just because two individual polygons have the same number of sides does not mean they can both tessellate. Additionally, a tessellation can't radiate outward from a unique point, nor can it extend outward from a special line. and even in paper towels!īecause tessellations repeat forever in all directions, the pattern can't have unique points or lines that occur only once, or look different from all other points or lines. You can find tessellations of all kinds in everyday things-your bathroom tile, wallpaper, clothing, upholstery. anything goes as long as the pattern radiates in all directions with no gaps or overlaps. They can be composed of one or more shapes. This month, we're celebrating math in all its beauty, and we couldn't think of a better topic to start than tessellations! A tessellation is a special type of tiling (a pattern of geometric shapes that fill a two-dimensional space with no gaps and no overlaps) that repeats forever in all directions.
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