I wanted to play with cellular automata for a while. When I saw the post about the contest, it finally got me into gear and I had some fun with rule 30:
https://brunni.de/findings30/
From the abstract:
The usual pattern starting from a single cell with state 1 / black is examined. It is contructed from a richer structure which yields a progression of polynomials for diagonals from the right. It is shown that each diagonal from the left can be expressed by the progression of polynomials for diagonals from the right and how the connection between left and right diagonals forces the diagonals from the left to eventually become periodic.
The necessary and sufficient condition for period doubling of diagonals from the right is established. It is also shown that periods cannot decrease. The result suggests that predicting period doubling is computationally expensive.
I suppose there is nothing new in there?