Tessellations

Tessellations will appear everywhere if you have built a habit of seeing them. In shirts, dresses, on the bed-covers, curtains, buildings, flowers, etc.

But mostly in nature we do not see tessellations but symmetry. So how tessellations and symmetry are related?

I remember butterfly wings which are symmetrical, and tiles in my home which repeat (or tessellate). 

The building block or tile used in tessellations is repeated over and over again to fill the whole space.

For example here are few tessellations with similar tiles:

Sometimes the shape used is similar but the way it is arranged or its colour is different. And that’s how different tessellations can be made using similar shapes. The detailed description can be found here: Tessellation symmetry

Triangles, squares and hexagons are the only shape which can tessellate regularly. And others can be made to tessellate for example by using two different shapes.

The work of Maurits Cornelis Escher is very famous in the world of art and mathematics.

M.C.Escher
Image source: http://www.mcescher.com/gallery/italian-period/hand-with-reflecting-sphere/

As written on the website of Tessellations:

During his life, he became obsessed with filling surfaces with pictures that did not overlap or leave spaces. Aged 68, he stated, “Filling two-dimensional planes has become a real mania to which I have become addicted and from which I sometimes find it hard to tear myself away.”

First Tessellation of M.C.Escher
Image source: http://www.tessellations.org/tess-escher6.shtml

He also made tessellation which grew smaller on the outside, and similarly in reverse.

Image source:  http://tessellations.org/eschergallery24.shtml

So let’s keep on seeing patterns in nature! Happy World Tessellation Day.