As you can see, as of late I opened a thread on n-disc operads:
Clarification regarding little n-discs operads
The thing is, those drawings there could somehow be construed in the real world as slices of mortadella or the like. This intuition can be helpful, I guess. The thing is, while having a look once again at Benoit Mandelbrot's book on fractals (the short version), after having read it some time ago, I have come accross some diagramms and structures in fractal reality and theoy he calls "Appenzell cheese slices with random round holes" and "Emmenthal cheese slices with random round holes", respectively. The basic idea seems to be biting rather than inserting or composing, but other than that, it looked to me like those operads. Am I right? Is there a reasonable relation?