To cut my teeth in coding, I often used chess as a subject to make simple programs. These included programs that reformat PGNs, or count the number and types of moves that occur in a game. It may also prove to be possible to apply mutual information to chess data, and see if certain move patterns or piece placements co-occur.
These tools are available below. In addition, you can view my chess puzzle book. When you are done having fun, remember: there is more serious science to be done!
PGN Reformatting: A self-evident tool, which allows to you change the format of different PGN sources.
Square Traffic: Given one or more positions or games, this will compile the number of times a particular piece moves to a given square.
Square Parking: Given one or more positions or games, this will calculate the number of positions (the residency) of a piece on a given square.
Chessboard Heatmap: This can take data from the above two tools (Parking and Traffic) and generate a nice heatmap for visualization.
PGN-2-FEN-2-COUNT: This is a expanded or deconstructed version of some of the tools above, allowing you to carry out the steps in the parking tool in piecemeal fashion.
Random Move Shoot-out: This will use some rudimentary engines to play one or more games against itself and report the results. Believe it or not, I first created this in 2015, before AlphaZero!