16 gleiche Dinge

You should have no problem finding 16 objects that are exactly the same. Try looking in the kitchen, in your craft drawer, among your toys or school things, or anywhere else in the house. Using only 16 objects, you can create a surprising number of patterns. A pattern is a structure which repeats itself. To begin with, arrange your objects into a regular square. The objects will always stay in the same place. But you can change the orientation of each object: turn it to the left (rotate by 90 degrees), turn it upside down (rotate by 180 degrees), or turn it to the right (rotate by 270 degrees).
Now you can come up with a plan or a design. For example, you can turn the first object to the right, the second to the left, the third to the right again, and so on. You can also do different things in different rows: in the first row, turn the first object to the left, the second to the right, and so on; in the second row, flip the first object upside down, skip the second, repeat; copy this sequence in the third row, then go back to the original left-right pattern in the fourth one.
Does this sound complicated? It certainly can be. But you don’t need any instructions at all. Just try it out: if it looks regular and pretty, then you have most likely created a pattern with a repeating structure.

Our first example is made with sixteen chocolate ducks.

Some objects make it difficult to see the underlying pattern.

Some objects do not give rise to as many patterns as others. Lego bricks are a good example.

Why is that so? You can definitely figure it out!

Finally, some objects do not give rise to any distinct patterns with our method at all. Can you think of objects like that? You’re sure to come up with something. (If you scroll all the way to the bottom of this page, you’ll find an example.)

Have fun creating patterns!