Logic Masters Deutschland e.V.

This puzzle was made as part of Scojo's imposter series. I made two versions of the puzzle, and while I think this is the better puzzle, I think the other one was more identifiably me, so I submitted that one to the game, but I'll be posting this one for public consumption. Thanks to Marty Sears for help with grid aesthetics. Please leave a comment if you enjoy it!


RULES:

Normal Sudoku Rules Apply

Each cell (with digit N) points to a cell in the grid according to the following rules:
1. The cell faces the same direction as going from 5 to N on the SudokuPad keyboard, or equivalently, in the direction from box 5 to box N (1 points NW, 2 points N, 4 points W, etc.). Cells with 5s always point to themselves.
2. The cell points to a cell that is N cells away. If moving orthogonally, the grid wraps around to the opposite edge. When moving diagonally, wrap to the other end of the same diagonal.
Example: A 4 in r1c3 would point to r1c8. A 3 in r1c8 would point to r6c3.

If a cell points at another, then both are in the same chain. Each chain is either wholly shaded or wholly unshaded. Shaded and unshaded cells form a valid yin-yang (that is, no 2x2 area is wholly shaded or unshaded, and all shaded cells are orthogonally connected, as are all unshaded cells).

Four complete chains have been given (one marked with red circles, one with blue squares, one with green diamonds, and one with purple ovals).