If the first stories in the Bible are any indication, this is a more difficult question to answer than it might seem.
Most of the traditions which are based on them — whether Jewish, Christian, or Muslim — draw sharp contrasts between the unpredictability and even capriciousness of human minds and the rock-solid unchangeableness of God’s.
The stories themselves, however, may suggest something else. For example, just when the human race was about to drown in a flood, the put-out God who was preparing to send it had second thoughts. Noah’s ark guaranteed that life on earth would start all over and that God would rage no more.
This is the same God with whom Abraham earlier negotiated a better chance for the people of Sodom and Gomorrah to escape punishment for a particularly vile group of sinners in their midst. In an Islamic re-telling of that story, it is the same God with whom Muhammad, encouraged by Moses, would negotiate a more realistic prayer requirement.
And it is this same God whom the prophet Hosea heard to “repent” of thinking about abandoning his people, even for their faithlessness.
But this is also the same God who handed down a law code by which his chosen people and then all of humankind would be judged, both on a daily basis and in final terms. And who promised later to inscribe it inwardly on human hearts (Jeremiah 31:33). What this promise really comes down to is that one day human obedience to divinely imposed laws will be as unwavering as the Lawgiver himself is.
For a faith based on obedience to divine law, the Law itself is the clearest sign that God never changes in what he expects of us and in what he is willing to tolerate in us. For a faith based on rejoicing over divine grace, however, love is the clearest sign that God never closes his mind to expect great things from us and to forgiving us when fall short.
A god worthy of being called God, or Yahweh, or Allah never changes in desiring the best in every possible world, and in seeking to communicate what that “best” can be in each. But in our world at least, this must be a God for whom openness to change is greater than keeping things as they are, and mercy is greater than judgment.