Patterns

​This is Maria. What are you doing Maria? I'm cutting. I'm going to tile the floor in my kitchen and I'm trying different patterns. It might be a pattern of squares, or triangles, or hexagons, or pentagons.

Wait a minute. This didn't work. With pentagons, there are spaces left, small rhombus shaped holes. What about eight corners? The octagon?

No, that doesn't fit either. Yes. Only three, four, and six-sided polygons can be put together in a pattern without holes. For all other patterns, you need extra pieces of a different shape in order to cover the whole floor without gaps or overlaps. What Maria is making is called a tessellation.

In a tessellation, one or more geometric shapes are placed together without gaps or overlaps. But patterns can be found not only in geometric shapes. Movements, thoughts and tones from musical instruments can also follow patterns, and colors. ​ ​I want to have patterns in different colors as well. ​ ​Okay, let's look at some of Maria's patterns in different colors. A pattern can be represented by the same colors repeated in a certain order. Another way to make a pattern is to make regular changes, where the difference is repeated.

In traditional Islamic art, there are plenty of advanced examples of tessellations, with patterns in both colors and shapes. Search for images of Islamic art, and you will find many beautiful mosaics. Patterns can also be made of other patterns. Small circles that together make a square, for example. Patterns of patterns.

If the same pattern repeats itself on larger scales, it's called a fracto. A fracto is a unique form of symmetry. The hole looks like a part which in turn looks like a part of the part. You can find fractos in nature. A leaf of a fern consists of smaller leaves of the same shape as the large leaf.

A crown of a tree is another example of a fracto where the same pattern is repeated on smaller and smaller scales. also, there is a type of broccoli called Romanesco. Look for it next time you go shopping. The surface of the Romanesco is a beautiful fracto. It makes tasty soup, too.

Now I know what the kitchen will look like. The floor will be made of bright octagons with darker squares in between. On the wall, I'll have a fracto. But not the Romanesco. It will consist of the circles with the smaller circles inside.

Pretty. Yes?