Tuesday, August 16, 2011

Zen Venn Garden

Venn diagrams are graphic representations of all logical relationships of a finite group of sets. What we see most often are two set combinations that show two sources, such as people interested in plants and people interested in venn diagrams. Where they overlap you have people who are interested in plants & venn diagrams.

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:

Thinking about how one would view the garden, I decided that I it might be better to incrementally sink the overlapping beds so you could get an overview of all the plants when standing at the top. I also had to choose some plants to fill those beds with. When I really started thinking about the overlapping plant traits, it was harder to think in terms of larger plant sets than I thought it would be, so I decided just to detail out a 3-set Venn garden. Agaves came to mind because I'm fond of their sculptural qualities, and they're the types of plants obsessive collectors really get into producing or discovering unique versions of plants with unusual traits. Here is the final, annotated rendering:

The overall effect of gazing down at a grouping of plants and focusing on their qualities, I think has a very Zen Garden quality of meditation, hence the moniker Zen Venn Garden. I guess the next step is the Euler Garden.