Friday, 2 August 2013

Houndstooth and other tessellations

I distinctly remember tessellations as the highlight of year eight maths, because it involves colouring, and pretty patterns. In simple terms, tessellation is tiling, where the tiles don't overlap and there are no gaps between tiles. Look at the ground while you're on a pedestrianised road - often, there's a pattern of interlocking bricks. That's a tessellation. Next time you're in a church, have a look at the tiling underneath your feet.

A semi-regular tessellation (using more than one regular polygon) on the floor of a Spanish church
From Wikipedia

The pattern of four-pointed shapes that make up houndstooth is a translation tessellation. Just scroll down to find out more about the types of tessellation. When the shapes are quite large, houndstooth makes for quite a busy pattern, so try to tone down the rest of your outfit. But if you're feeling brave, try mixing and matching a smaller houndstooth, which is quieter, with other patterns and textures.

There are three kinds of tessellation: translation, rotation and reflection. To show you these, I've used tessellations by M. C. Escher, a Dutch artist known for his maths-inspired works, like impossible triangles and circular waterfalls and upside-down sideways right-way-up staircase labyrinths.

Translation: each scarab beetle is identical, and are neither rotated nor flipped.
By Escher
Rotation: the fish are repeated but rotated. Look at where the noses of four fish meet, which is also where the tails of four opposite-coloured fish meet.
By Escher
Reflection: all the white riders face one way, but the orange riders face the opposite way - they're reflected.
By Escher

1 comment:

  1. i love all the prints , always a delight to check out your blog sweetie ,

    I Just posted a shopping haul & a great news for all my followers , wanna see it ?



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