In the following we are assuming that you are familiar with the game 'Floor Tilings'. 'Aperiodic Tilings' uses more or less the same functions (apart from the copy functions). Hence only the copy functions will be explained here again.

It is very easy to create aperiodic (i.e. non-repetitive) tilings from self-similar polygons. This is the method we use here and this is also the method which the famous 'Pinwheel Tiling' uses; see history text for details. The method creates patterns which are on the line between order and chaos. This makes them visually pleasing.

As you can see on the board, we start off with a simple shape, in this case a domino, which can be tiled by smaller copies of itself. These smaller copies have all the same size in this case, but this is not necessary in general.

The second drawing shows a domino twice the size of the first, and tiled with 4 smaller copies of the first. The third drawing shows a domino twice the size of the second, and tiled with 4 copies of the second.
If we produce bigger and bigger dominoes this way, we will cover bigger and bigger areas. The resulting covering of the plane will be indeed aperiodic. We make this more visible by colouring the second domino with 4 different colours and keeping these colours when we make copies of diagram 2.

Your task is to try to repeat the suggested process until the given 50x50 board is fully covered.
The four templates shown at the right border help you with this. Using them you can draw a 2x4 template made from four dominoes with each click.
The HOTSPOT option allows you to change the location of the handle on the template. For some variants the hotspot is fixed.

The solution (select Help/ShowSolution) will show you what your result should look like.
Depending on into which direction you enlarge the domino with each step, the outcome will look slightly different. When you have covered a large area this way, click 'delete all outlines', then click 'add all outlines' to create some interesting patterns.
It also pays sometimes to make 2 or 3 colours the same first (use button 'exchange colours').

Variants: In some variants (such as variant 3) one has to alternate between two dissection methods with each 'generation' of enlargement in order to obtain a aperiodic pattern.

There is also a FREEPLAY variant with an empty board.

The most famous aperiodic tilings of the plane are most probably :

• the 'Pinwheel Tiling' attributed to Charles Radin, featured on the Melbourne Federation Square Buildings (http://astronomy.swin.edu.au/~pbourke/texture/pinwheel/). The pinwheel tiling is of the self-similar type discussed in this game. It is derived from a right triangle with sides 1 and 2 tiled by five smaller copies of itself.
• Roger Penrose's quasi-crystals with near-fivefold symmetry.