Patterns suggest other patterns, often yielding patterns of patterns.
However it isn't immediately apparent that this patently visual reference to patterns applies to all of mathematics. Many of the higher order relationships in fields like number theory defy pictorial representation or, at least, they don't immediately lend themselves intuitively to a graphic treatment. Typically real insight into such problems has come directly from the mind of mathematician who ferrets out their essence from formalized representations rather than from the data. Consequently, patterns of a new sort are beginning to appear in the morass of numbers. However the epistemological role of computational visualization in mathematics is still not quite clear, certainly not any clearer than the role of intuition where mental visualization takes place.