Knuth's TAOCP's latest published part, Volume 4 Fascicle 6, on Satisfiability contains a number of visualizations that really are amazing and worth just buying a copy of the book for, just to ponder over these images.
The satisfiability problem of whether there exists an assignment of boolean values that makes a given boolean formula evaluate to TRUE is, IMO, truly a fundamental problem in computer science.
Any piece of code with some inputs and outputs can be transformed into a boolean formula (albeit a huge one). This process feels akin to expressing molecules, from simple ones like H2O, to the highly complex proteins that make up much of our Cells, in their constituent atoms and more importantly the atom interactions.
Knuth (EDIT: Actually, Carsten Sinz) takes this concept one step further and produces visualizations of non-trivial boolean formulas that clearly show the regular, both symmetrical and asymmetrical, sometimes fractal-like nature of these formulas.
In my mind, these visualizations are quite powerful and strikingly show the fundamental building blocks of (digital) computation.