FIBONACCI

Copyright (c) 1990 Thomas Naylor

This game is played on the following board:

 
PIECES - Each player has one center piece (in the diagram, the marked stone), six strike pieces (the other stones in the first row) and six support pieces (the red stones for Black, the green stones for White).
GROUP - A connected set of friendly pieces.
TURN - On the first three turns, Black moves 1, 3 and 5 times, while White moves 2, 4 and 6. On the remaining turns, each player moves 6 times.
Exception: For each strike piece adjacent to his center piece, the player loses one turn move.
MOVE
A strike or support piece may move to an adjacent empty cell, or to a cell (either empty or occupied) adjacent to the group it belongs. In the second option, if it moves to an occupied cell it displaces the other piece (either friendly or not) to the cell it came from.
Center pieces cannot move, they can only be displaced. 
GOAL - Wins the player that surrounds the opponent's center piece with his strike pieces.

I placed this game on the Towers section, since there are 3 types of pieces that can be emulated by stacks of different sizes.

Some strategy tips from the author: (a) Get your strike pieces in as quickly as possible adjacent to the opponent's centrepiece - thereby reducing his movements and paralysing his pieces. (b) Use both your strike and support pieces to scatter your opponent's groups by displacing his pieces to the ends of your lines. (c) Make sure that when you attack you attack to great effect - otherwise you’ll be left too close to your opponent's pieces, and your pieces will be scattered on the next turn.

More information can be found at this webpage (where is also possible to buy a game set).