**Some Venn diagrams** can be expanded indefinitely to form infinite fractals. Here are some examples, I've just shown the tops as I haven't got the patience to draw the full infinite diagrams.

Infinite Venn Diagram |
Venn Diagram combinations of A,A,A,B,B,B,C,C,C,D,D,D |
Venn Diagram combinations of A,A,A,B,B,B,C,C,C,D,D,D,E,E,E |