Are human brain processes, like intuition, creativity, imagination and the ability to create art, algorithmic processes (that is, produced by an algorithm)?
The answer to this question can be very subjective and depends upon the situation. Scenario 1: When we were toddlers, we learnt a new language(our mother tongue) automatically just by listening to the people around us talking. We did not have to put much of any efforts into this. A similar situation is, when we practice something, we tend to get faster and more accurate in that than before, automatically. Scenario 2: When we think about something creative, or make some decision, we don't always follow a defined way, and can even come up with ideas which was not there before.
In short, processing of human brain is as complex as it can get. Defining any process algorithmic, puts a strong bound on it's scope, and the working of brain is way beyond than that.