This is a Heyacrazy puzzle.
Rules of Heyacrazy:
Shade some cells of the grid.
Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected.
When the puzzle is solved, you must not be able to draw a line segment that passes through two borders, and does not pass through any shaded cells or grid vertices.
For an example puzzle and its solution, see this question.
Starting in the top right, these two squares are the only options that don't allow that fork to make lines, and also don't block off the top right square.
Next, the fork below it has to be this way, as the other can't block off the line between it's handle and the bottom of the big fork. We also fill in some of the bottom squares they don't get orphaned.
Continuing, we fill in these two as they're the only options to block off a line to the line directly below the top right square.
Next, we fill in this one to block off lines across the big fork.
Lastly, we fill in the final bits. We have to move the left of the 2 squares up one from how we filled in the similar fork so that it doesn't orphan the corner square.
