[Patterns from] bitwise functions
Bitwise functions typically yield nested patterns. (As discussed above, any cellular automaton rule can be represented as an appropriate combination of bitwise functions.) Note that BitOr[x, y] + BitAnd[x, y] == x + y and BitOr[x, y] - BitAnd[x, y] == BitXor[x, y].
The patterns below show where BitXor[x,y]<=t for successive t and correspond to steps in the "munching squares" program studied on the PDP-1 computer in 1962.
Nesting is also seen in curves obtained by applying bitwise functions to n and 2n for successive n. Note that 2n has the same digits as n, but shifted one position to the left.