'Influence' is a curse of art criticism primarily because of its wrong-headed grammatical prejudice about who is the agent and who is the patient: it seems to reverse the active/passive relation which the historical actor experiences and the inferential beholder will wish to take into account. If one says that X influenced Y it does seem that one is saying that X did something to Y rather than that Y did something to X.
But in the consideration of good pictures and painters the second is always the more lively reality. It is very strange that a term with such an incongruous astral background has come to play such a role, because it is right against the real energy of the lexicon. If we think of Y rather than X as the agent, the vocabulary is much richer and more attractively diversified: drawn on, resort to, avail oneself of, appropriate from, have recourse to, adapt, misunderstand, refer to, pick up, take on, engage with, react to, quote, differentiate oneself from, assimilate oneself with, copy, address, paraphrase, absorb, make a variation on, revive, continue, remodel, ape, emulate, travesty, parody, extract from, distort, attend to, resist, simplify, reconstitute, elaborate on, develop, face up to, master, subvert, perpetuate, reduce, promote, respond to, transform, tackle ... everyone will be able to think of others. Most of these relations just cannot be stated the other way round - in terms of X acting on Y rather than Y acting on X.
To think in terms of influence blunts thought by impoverishing the means of differentiation.
from Michael Baxandall, Patterns of Intention: On the Historical Explanation of Pictures
(quoted in Edward Tufte, Beautiful Evidence)