Morphing tilings are sets of tilings which change from one tiling pattern to another. This can happen in many ways:
- as a related set of tilings which change like an animation
- as tilings where the change is seen as you move around the page
To create them you need to go through the following stages:
- take a regular tiling
- add a motif to each tile to create a new tile
- change the motif to create a morphing tiling
This is an example of just one type:
Take a square grid:
- the motif can be replaced
- by a variation of the motif (for example a rotation)
- by replacing it with another related motif
- the motif can be distorted by transforming or positioning the points.
Combining these with the way in which the motifs are mathematically related when they are changed gives rise to millions of new tilings.
The following are some tiling examples, and there are more in subsequent posts
This is a replacement morphing. There are four tiles, based on four orientations of a motif:
Replacement is then made cyclically:
A B C D becomes B C D A becomes C D A B becomes D A B C.
So the set of tilings is:
Why are the first and third a similar looking pair, and second and fourth also?
How are the pairs similar?
What other possibilities could you use as a replacement?
This is a different type of replacement morphing. There are three types of motif, each of which can exist in two orientations. In the replacement, each tile is substituted by an equivalent tile showing a different motif.
This is an example of a tiling where the motif is changed as the tile is placed.