As a caveat, i am not a mathematician but rather a programmer with an amateur interest in patterns, fractals, sequences, data science.
That said, i have been following recent developments in aperiodic tiling with interest.
I've had an idea for an application for it, but I don't know enough in the field of mathematics to know if:
- It's obvious, been done, move on
- It's an interesting idea worth exploring, or
- It'll never work or be useful, just stop now.
The thought is as follows:
- By definition, aperiodic monotiles don't repeat on the plane, therefore
- They are effectively a visual representation of an infinite, non repeating sequence.
- They can be computed relatively easily (e.g. see here), and the next tile can be calculated based on the position of the previous one.
- Therefore, you effectively have a pseudorandom number sequence, given a seed of the coordinates to start at.
Is this worth exploring, or just a rabbit hole leading to a dead end?