Simple examples of what I have in mind:
Cracks: primes as falling through "the cracks" in the Sieve of Eratosthenes.
In Between: the items "a" and "I" in English being both letters and words.
Background: the configuration of whitespace in a text file.
Noise: the necessary difference in resolution (definition) between film or video and live viewing.
Interface: Instruction Repertoire as the interface between computer hardware and software.
My interest in these areas was motivated by an analytic quest into "what is pattern", which in turn was motivated by reading Robert Pirsig's explanations of his "Metaphysics of Quality" in his book "Lila". It quickly became apparent on first look that pattern consists of repeated alternations of more-varied/interesting "content" with less-varied/interesting "separators". This is a highly general observation: two examples of separators are whitespace in text documents and cell walls.
The thesis is that the separators are too-often ignored or invisible and that they are more important than usually acknowledged -- that things are not always as they seem in this regard (foreground/background).