Tuesday, February 2, 2010

Transformation Tessellation Tuesday (with a nod and a wink to LoveBug Studios*)

Today, I will discuss tessellations and how to transform them . . .

What is a tessellation? A tessellation is "one or more congruent geometric shapes that cover an infinite plane without gaps or overlaps." Huh? How about "one or more shapes that fit together to make a repeating pattern"? The Dutch graphic artist, M.C. Esher (my hero), is well-known for his tessellations.

I will begin with my design tile arranged as a 9-patch block . . .

All nine tiles maintain the same orientation, that is, they are all facing the same direction. This is an example of the operation of symmetry called Translation. Any given tile can be shifted up, down, left, right, or diagonally onto its neighbor without changing the overall pattern.

Speaking of pattern, do you see the Shape outlined below? (Notice that I refer to this as a capital "S" Shape.)

This qualifies as a tessellation because it is a single Shape that fits with itself to make a repeating pattern. Here are four 9-patch blocks, with complete Shapes outlined.

Let's take another look at the basic Shape . . . it is made up of six contiguous shapes, that is, six smaller shapes that touch each other. In fact, these are the six shapes that make up the original design tile!! One shape each from six different design tiles make up this larger Shape. (These individual shapes are lowercase "s" shapes.)

Here's where the "transformation" comes in . . .

Below, I have shaded in the shape at the bottom of our Shape . . . I have also shaded in the same shape at two other points where they touch the Shape.

By using one of the alternative shapes, I can make two different Shapes that are also tessellations.

Try it yourself with one (or more) of the other shapes in the Shape . . .

Next week: how to transform multiple-Shape tessellations!!

*You can check out LoveBug Studios here . . .

As always, thank you for reading my blog . . . please feel free to leave a comment or follow this blog!!


  1. Interesting post Raymond. You've given me more info to read, chew and digest... Now off to the other posts. I'm still your biggest fan!

  2. Thank you, Greg . . . I've found inspiration, and will explore "tessellation territory" further in the weeks to come . . . grab your pith helmet and machete, and follow me!!

  3. I have a pink 'hello kitty' helmet and a box knife.. will that work? LOL

  4. Thanks Raymond for the nod & for giving a lesson on tesellations. I'm always trying to find pleasing shapes in the designs, you are showing how it can be done without necessarily needing to turn a tile.

    All I have though is a rotary cutter and a plastic FQ container. I suppose I could wear that on my head, but what will I do with the FQs?

  5. Hold onto the FQs for the time being . . . inspiration may strike at any time (and the FQs will make a nice cushion to soften the blow), LOL!!