What is Tessellation?

The word tessellation may sound scholarly and forbidding. It's not. Tessellating is as simple as tiling a floor.

Square tiles repeated over and over will cover a floor without any gaps. 

This is a tessellation.

Triangular tiles, like these, will cover a floor without gaps.  This is a tessellation.

Octagonal tiles leave gaps that have to be filled with diamonds.  This is not a tessellation.

These oddly-shaped tiles will cover a floor without any gaps (the gaps around the outside edges don't count).  This is a tessellation.




A tessellation is a pattern that uses a single repeated shape to completely cover a surface without gaps.

If we forget about floors and think about quilts, then a whole new world of quilt design opens up to us.

Playing with Tessellation

What if I create a block on a nine-patch grid that looks like this?  Can I use it to make a tessellation?




This won't tessellate because it consists of 2 different shapes and tessellations must have only one repeated shape.  Can I change it so that it will tessellate?

What if I create a second block with the colors reversed?

Then, what if I take 2 of each block, arrange them like this, and then join them to make a larger block?  Will the larger block tessellate?

It does. The black and grey areas are identical, so only one shape is being repeated.

The tessellation is more apparent when the block is repeated, as in these 2 examples.

 

What if I start with something only slightly different?  Again I'm using a block  and then repeating it with the colors reversed.

What if I take 2 of each block and, as before, arrange them in a kind of pinwheel?

The light blue and dark blue areas are identical.  Only one shape is being repeated, so this will tessellate.

Here are 2 examples of this larger block being repeated. This time the tessellating shapes are larger and more detailed.

What if I start with this block and its reverse block?

What if I rotate 2 of each block and then combine them?

The white and blue shapes are identical; this will tessellate.

These examples of the larger block being repeated are even more intricate and interesting.

 

This approach to creating tessellated patterns is beginning to show potential. I'll have to pursue it further some other time.