CASCADES 

Copyright (c) 2001 William Chang

The game is played on the following hex board, with the following setup:

DROP - Each stone is dropped on an empty cell, next to and below a stone of the same color MOVE - First player drops one stone at the first turn, then each player drops up to two stones (he may pass).  GOAL - Wins the player with more stones on the bottom row.

Some words from the author: For some time now [Apr 16, 2001] I have been toying with the idea of trying to model/abstract the flow of water carving out a mountainside. A related geometric pattern is the fractal on certain seashells. [...] The image in my mind is a root-pattern forming or tributaries of a river. [...] The game generalizes to any MxN board. Without more experience playing and "figuring it out" I don't know how M and N affect playability. My intuition suggests 8x8 (really 8x15 if you measured it at the bottom) is already nontrivial and 10x10 might be "tournament".

An example On the left, the game is already defined. White does not need to worry at this point with is top left stone, since the bottom left cell cannot be taken by Black. The same happens with the next 3 bottom cells, which are Black, whatever White plays.

[author words] After the bottom row is filled, the game can be continued where the board progressively _narrows_ instead of widens. This variant can also be arranged in a ring with a predetermined starting position and stones (dry streambeds?) flowing toward a central "lake" (which may even be empty, in which case whoever occupies the center wins).

 . . . . . . . . . . .           x o x o
  . . . . . . . . . .           o . . . x     Too small
   . . . . . . . . .           x . . . . o    of a board!
    . . . . . . . .           o . .   . . x
     . . . . . . .             x . . . . o
      . . . . . .               o . . . x
       . . . . .                 x o x o

I have named this game BigBasin, after a local mountain formation in Northern California. (It could have been called Tahoe or something.) I think more work needs to be done here than in Cascades. [...] The family of games I call Cascades and BigBasin are attempts at creating an abstract theme game based on a ubiquitous pattern, the flow of water.  [William Chang Los Gatos, California 16 April 2001]  (C) 2001 William I. Chang

The author also suggests a variant: Stones can be dropped at any empty cell, but a stone cut off from receiving (downward or sideways) flow (i.e., if there is no possible path to connect it to the top row, and there is no consideration of future enemy stone captures) is immediately removed. Another change would be to score all territory occupied, instead of just counting the bottom row.

There is a ZRF to play Cascades with Zillions.