This idea of overlap got me thinking about hybridization of plants that has been practiced by farmers and nurserymen since the dawn of agriculture to produce more desireable varieties for human consumption, whether edible or visual (see Michael Pollan's Botany of Desire). Why not celebrate this hybridization with a garden that starts with a finite set of plants each with a featured trait (ie. variegated, dwarf, purple-leaf, etc.) and then add additional plants where these traits overlap. So you end up with your very own Venn garden. In my Venn garden experiment I decided to take the planting bed layout very literally, because I think that Venn diagrams themselves have interesting shapes. Here are some diagram examples for different types of sets:

3 set

source: http://en.wikipedia.org/wiki/Venn_diagram

4 set

source: http://en.wikipedia.org/wiki/Venn_diagram

6 set

source: http://warpinghistory.blogspot.com/2010/04/finding-antipodes-mathematical.html

7 set

As you can see, they can become quite complex, and I decided to start off with examples of three and four sets. Some CAD drafting and Sketch-Up importing left me with these two raised planter diagrams: