Nautilus chess piece

The Nautilus is a custom chess piece that incorporates a unique movement inspired by the Fibonacci sequence and the concept of spirals.

The Nautilus performs a series of orthogonal jumps (vertical or horizontal), following specific rules:

1. Fibonacci progression:
The first jump is 1 square, the second is also 1 square, the third is 2 squares, the fourth is 3 squares, the fifth is 5 squares, and so on.

2. Direction change:
After each jump, the next must be perpendicular to the previous one. For example, if the Nautilus jumps forward, the next jump must be to the left or right.

3. Rotation direction:
At the start of its turn, the player decides whether the Nautilus will follow a clockwise or counterclockwise direction. This direction must remain consistent throughout the turn.

4. Turn ending conditions:
The Nautilus's turn ends when:
- The player chooses to stop the movement.
- It captures an opponent's piece.
- It cannot perform the next jump because the square is occupied by a fr