  Sprouts is a two-player topological game, invented in 1967 by Michael
Paterson and John Conway. The game starts with p spots drawn on a sheet of
paper, and lasts at most 3p-1 moves: the player who makes the last move wins.
  Sprouts is a very intricate game and the best known manual analysis only
achieved to find a winning strategy up to p=7 spots. Recent computer analysis
reached up to p=32.
  The standard game is played on a plane, or equivalently on a sphere. In this
article, we generalize and study the game on any compact surface.
  First, we describe the possible moves on a compact surface, and the way to
implement them in a program. Then, we show that we only need to consider a
finite number of surfaces to analyze the game with p spots on any compact
surface: if we take a surface with a genus greater than some limit genus, then
the game on this surface is equivalent to the game on some smaller surface.
Finally, with computer calculation, we observe that the winning player on
orientable surfaces seems to be always the same one as on a plane, whereas
there are significant differences on non-orientable surfaces.
