![]() ![]() Escher tessellations are complex and intriguing. Like many other repeating or geometric designs, tessellations are rooted in mathematics. Math divides tessellations into three main categories: regular, semi-regular, and demi-regular (other). Regular tessellations in math are shapes like squares, triangles, and hexagons that fit together precisely. You could cover a flat surface with these shapes of the same size and not have any white space between.Ī semi-regular tessellation is made of two or more kinds of shapes. Think of octagons within squares in between them, or a 7 sided polygon (heptagon) with star shapes between. Alone, the octagon or 7 sided polygon wouldn’t tessellate, but with the insertion of another shape, they can.ĭemi-regular tessellations are those that use non-regular or non-geometric shapes, such as those popularized by M.C. Tessellations in NatureĪ honeycomb is a perfect example of a tessellated pattern in nature: tiny hexagons repeated without gap or overlap. So are the diamond-shaped scales of snake skin and the knobbled surface of a pineapple. While you won’t find many other examples of precise, mathematically accurate tessellated patterns in nature, various organic patterns come close and can be used as inspiration for creating tessellated patterns. Think: the unfurling petals of a flower, birds’ feathers, or pinecones. ![]() Tessellations have been used for centuries, and across cultures, in various aspects of design. Think of tiles or mosaics used in Ancient Rome, medieval Persia, or Morocco. In modern design, no single artist has been as influential as M.C. The work of the Dutch graphic designer became especially popular in the late 20th century and after. Escher was inspired by math and the tessellated Moorish design and architecture of the Alhambra in Southern Spain. He used mathematical grids as the basis for creating complex interlocking designs. His work shows how creative it’s possible to be with tessellated patterns while following mathematical principles of order and regularity. If you’d like to learn how to create a tessellation pattern, there are a couple of ways to do so. Shapes can be tessellated freehand on paper or using graphic design computer programs. Tessellating freehand will take much longer, but can be done if you have patience or don’t have access to advanced programs. Otherwise, follow the steps below to learn how to tessellate a square shape with a pattern inside it in Photoshop and Illustrator. ![]() Similar principles can be applied to tessellating other shapes. If you’re not already proficient in using these programs, take an introductory or refresher course before you begin learning how to make tessellations. The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP.Step 1: Sketch Out a Rough Idea on Paper Sketch a line outline of the components of your tessellation first.What is the length of the line segment joining points B and F?.Use the above figure to answer the questions that follow: He used regular octagons, squares and triangles for his floor tessellation pattern To ensure accuracy in his work, he made the pattern on the Cartesian plane. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.Ī craftsman thought of making a floor pattern after being inspired by the above design. You may find tessellation patterns on floors, walls, paintings etc. Historically, tessellations were used in ancient Rome and in Islamic art. A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. ![]()
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