#py5

[szimmetria-airtemmizs]

On the sides you can see two curves of constant width, that is a curve whose width is the same in all directions. This is the reason they always touch the two lines as they rotate. The existence of curves of constant width is well known by now. What is much less known is that you can morph between any two such curves such that during the morph the curve stays a curve of constant width. For these two curves the morphing can be seen in the middle. (Actually, you can see two different morphs. )

[szimmetria-airtemmizs]

Black and white.

[szimmetria-airtemmizs]

It is always interesting how a small change can completely change the mood. Compare this animation to my previous one:

[szimmetria-airtemmizs]

I always liked complex patterns that were created using a single tile. For example, the following pattern looks rather complex at first glance.

But it is actually created using a single hexagonal tile.

The idea came from a board game called Palago which uses exactly these tiles. Here is the middle part of the pattern using actual tiles. Unfortunately I don't have enough tiles to create the next level.

Another interesting property of this pattern is that it can be extended into an infinite pattern which is aperiodic. This pattern shows up for example in the tiling of the aperiodic tile found by Joshua E. S. Socolar and Joan M. Taylor. (Not to be confused with the recently found aperiodic monotile by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss)

[szimmetria-airtemmizs]

Orbit.

[szimmetria-airtemmizs]

Morphing between the different levels of a recursive pattern.

[szimmetria-airtemmizs]

Just some blobs.

[szimmetria-airtemmizs]