Experimental mathematics colloquium: Generalized animals
Sebastian Nielsen and Rasmus Mølck Nilsson
An axb animal is a con figuration of axb tiles where a and b are integers. Furthermore:
- Every translated tile has its corners in ZxZ.
- The translated tiles intersect only at their boundaries.
- The confi guration generates a connected set even after ZxZ is removed.
The aim of our project was to investigate properties of the growth rates when looking at the total number of axb animals with n tiles for various a and b, while n is fixed. We have written computer procedures that count these numbers.
We discovered some very nice polynomials that exactly computes a lot of these numbers. However we discovered that for a larger number of tiles there seems to be a systematic revolt aginst this description, a rebellion that may grow stronger as n increases.