The way I understand it, with quilted or curly Maple the figuring you see is actually cross-sections of end grain. The wood grows wavy, so when it's cut straight through, it alternately exposes straight and grain ends. End grain is more absorbent than straight grain, so if you dye it and then sand it back, the end grain retains dye in intra-cellular areas while the straight grain sands off and leaves new, unstained cells exposed. Maple is a closed cell wood, so the straight-grained parts don't retain any dye in the cells themselves. This is part of the reason Maple can be a real pain in the shorts to stain in the first place. It can easily end up blotchy, which is why it's recommended that it be sealed before staining so the take-up is uniform.
Birdseye, I'm not sure about. I think that's the result of environmental conditions that trick the tree into sprouting a jillion little branches, so all those "eyes" are actually little knots, where a little branch started out. But, I'm just guessing. If that's true, though, then I suspect there's enough of a difference in wood density/hardness at the "eye" that it wouldn't take stain/dye as readily as other areas.
I've seen some nicely done colored birdseye, but I suspect they covered it with a tinted finish rather than staining the wood itself.
