Look at it too long and my eyes go funny.
But very interesting
I know. The brain questions how it can see something like an infinitely interlocking floor that never repeats. I don't even know if it's possible to incorrectly fit them together, as long as you get three to interlock.
It makes me wonder what the effect on rotational conformity would be if you were to forcibly rotate with enough energy to force the surrounding tiles to rotate until the group reached a different configuration from a given point?
Let's say I flip a *single* tile. Starting with all tiles it borders on, how will the neighboring tiles have to move to conform at the lowest total amount of group rotation?
How much rotation does it take the next layer? And the next? And the next?
How many layers will I go through before the shape conforms to the new "center tile" without needing additional rotation?
What does this look like if we explore the set of states wherein a more rotated inner layer would allow for completion? Ie, does the system adapt to absorb any such single change?
What is the minimum change size to produce a requirement to continued conformity changes?
Is there any size of conformity change that will force a systemwide modification that will continue indefinitely?
If you zoom out far enough, and treat the tile colors they use as RGB or CMYK or whatever, will you find a region that tells a story comic book style beginning to end? What would the region of the tilespace around that even look like? Would it contain other similar comic book stories? Or are there infinitely many regions that contain that comic book, some weird and some spookily sensible?
The implications of this aperiodic behavior of a tiled surface are absolutely hilarious.
Considering the Chevron system, is there some way to guarantee breaking a periodic Chevron field(s) this way?
What is the radius of any given break on the symmetrical Chevron field(s), if it's impossible to break a given periodic field indefinitely into an aperiodic one from a conformity change?
Is there any conformity change to the aperiodic hat Chevron field that will shove it into periodicity?