When I was a kid I tried to make n-dimensional 'venn-like' diagrams, based on some magic formula that involved cutting a circle into n+1 slices, and connecting the dots in some way that always created the right number of sub-sets and never duplicates

Intuitively, I seemed to think it could work, but I never finished the algorithm beyond four sets because, as others have noted, large-set venn diagrams suck, and you should pretty much always use a heatmap :P :)

Please rethink how you want to present this data. If you try to Venn >= 4 sets the human brain can't make sense of the image (unless there are some disjoint sets present)

Yes, don't do it!

Or make a pie chart instead.

Just kidding about the pie chart.

Try this--way better than a Venn for this situation: http://vcg.github.io/upset/about/ UpSet is really neat, and designed exactly for the problem that Venns do not scale well in genomics type of data sets.

I sympathize with others suggesting not to do it. However, you might want to check out this thread Venn/Euler Diagram Of Four Or More Sets in particular Alex Reynold's answer.

1. Like anybody else I would not recommend doing this
2. but I want to share this interesting paper about 11-way Venn Diagrams because it has pretty pictures (which also kind of show why you should not use it in my opinion)