"In computer science, the term idempotent is used more comprehensively to describe an operation that will produce the same results if executed once or multiple times."
Which is more that f(x) == f(x) == f(x) for the state affected by f.
new_state = f(old_state, x)
f(f(state, x), x) == f(state, x)
draw(draw(fbuf, wnd, x, y), wnd, x, y) == draw(fbuf, wnd, x, y)
If we start in state x, then apply operation f, the resulting state is f(x). If we apply operation f again, we'll be in state f(f(x)). If f is idempotent, then state f(x) and state f(f(x)) are identical.