Then, the tessellations with one or two directions may have their motifs reflected. Type 4 in four directions and type 6 in six directions. Type 3 will have its tiles in three directions, Type 1 will have all its tiles in the same direction. There are six possible directions, and therefore will be six original types. Visually, what characterises first a tessellation is the number of directions taken by the motifs. This round of lovers is just waiting to grow! He wrote the first printed treatise on perspective, published in 1505. … No more, for instance, than copying Jean-Pélerin* that makes a drawing in perspective.Īnd if, as I hope, you are inspired to do figurative ‘tiles’, throughout the following pages you will find how to give birth to them.Īnd when, after some difficulties, you successfully make one, you will experience a great feeling of joy and humility before this "PARCEL OF INFINITY". I hope that what follows will make you realize that there are an infinite number of possible figurative motifs.Ěnd it is not just copying Escher to Judging by the few artworks coming from others. This method, taken from my book "PARCELLES D’INFINI", offers a walk in the garden of the regular division of the plane that Escher explored in many directions. "I walk around all alone in this beautiful garden, which certainly does not belong only to me, but whose gate is open to everyone." However, on the other side I landed in a wilderness and had to cut my way through with a great effort until - by a circuitous route - I came to the open gate, the open gate "A long time ago, I chanced upon this domain in one of my wanderings I saw a high wall and a premonition of an enigma, something that might be hidden behind the wall, I climbed over Have their own will, and it is they which guide It seems it is not I who am doing the creating, I have such sensations all the time when I am working on designs The hexagon is the smallest geometric figure which makes the lizard tessellation possible with a single pattern."The inventor has, all of a sudden, the distinct feelingĪlready existed before to have never been thought in the human brain. We need all six triangles to make the Escher's tessellation complete. The poor beasts made from this triangle would not have limbs on the right side. Of course, we can tessellate this triangle (or any triangle cut out from original drawing) but it will not produce lizards. Let's check for example the triangle made with vertexes where all three lizards heads meet: How do we know a triangle would not suffice? Because then each triangle has to have a different pattern painted on it and we need six such triangles. You might be tempted to think a triangle would suffice to make lizards because we may divide a hexagon into six triangles. Here is a movie how to deform the hexagon to get the lizards: Remember that you can create subpatterns (smaller ones) or superpatterns (bigger ones)Īctually this lizard is created on the basis of a hexagon, not a triangle! Here is the hexagon: Here the "deformation" of the grid is extreme, the grid itself has its own new shape: But art is about taking the resources you have as a guideline, not as a limitation. You have some other resources like mirroring, rotating, and scaling. Where you can see how he used a two-axis grid rotated 45° next to a work using a three-axis grid. Here is a screen capture of the website: Let us explore how Escher used these grids to develop part of his work. When you are using a pattern, you let the pattern guide you.Įdited some years later. Metamorphosis.Īdditionally, comparing two lizards they are not exactly the same. Especially if the next lizard will turn into a duck. I would probably have a reference drawing but draw those by hand. Look at the second image, it clearly marks the middle of the triangle and where the legs should intersect them. I really see no difficulty to draw this lizard by hand. You can also see these patterns in 3D often used in Architecture. We called it "Little Squares 101" Or "Sticks and Balls II" (That was the second course) and yes, we drew this by hand. This is a typical example of introductory classes at the University. Grab a paper and a ruler, draw some pages and find some more patterns! Look how many patterns you have with this triangular grid. We are used more to a square pattern, but this triangular pattern can produce hexagonal and rhomboidal patterns as well.Īnd you can play with it to start building ripples, but still, you repeat the internal objects on this now deformed patterns. These patterns are pretty easy to draw, and they are used for example in architecture in different cultures. You can have and use sub-patterns or smaller ones to be more exact. Once you know what to draw on each piece, you need to repeat this.
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