Boolean Rithmomachia

This game was inspired by the medieval game Rithmomachy. But whereas in traditional Rithmomachy the pieces are labeled with natural numbers and captures are based on arithmetic progressions and geometric ratios, in Boolean Rithmomachy the pieces have binary nybbles 0000, 0001, ..., 1111 and captures are based on the logical operations AND, OR, XOR, NOT. For good measure, the board has also been updated from two dimensions to three.