I’ve seen this asked in a few places recently. The idea is to end up with something that looks like this:
Notice how the border between the white and black shapes perfectly follows the curve of the shape underneath. This style can be really good for logos, as well as for more abstract designs.
The usual way of achieving this is to expand any strokes, divide all the shapes using the pathfinder, then manually select and color the pieces. This works, but can be tedious if you have many overlaps–in just this small example, it results in 11 different shapes. It also makes the image really hard to edit afterwards. There’s an easier way.
3. Make all the shapes white. I’ll change my circle and heart to have a white fill, and my wavy line to have a white stroke. Now you can’t see any of them:
4. Open your transparency panel under Window–>Transparency. Select all shapes, then set the transparency of all of them to “Difference”
Done! The finished shapes are still intact:
You can still move things around, and all the black and white areas will adjust as you move them.
Now go play with it! The inverted areas will always move themselves as you go. Add or delete shapes, add text, move things around! This works with strokes, filled shapes, even text! All of it can be edited on the fly, with all the inverted areas fixing themselves as you go.