Visible parts and projections of the affine fractal percolation

We study the visible parts and orthogonal projections of the affine fractal percolation. We show that for the affine fractal percolation $E$, conditioned on $E\mathrm{\ne }\mathrm{\varnothing }$, almost surely the dimension of the visible part is equal to $\min \{1,{\dim }_{\mathrm{H}}E\}$ from all directions except for the major contracting direction. The visible part from the major contracting direction is notably different from the other directions, and we provide a formula for its Hausdorff and box dimensions. In addition, we show that almost surely conditioned on $E\mathrm{\ne }\mathrm{\varnothing }$, ${\dim }_{\mathrm{H}}\pi (E)=\min \{1,{\dim }_{\mathrm{H}}E\}$ for every orthogonal projection $\pi$ excluding the one onto the major contracting direction, and given ${\dim }_{\mathrm{H}}E>1$, these projections contain intervals.