The phrase "most irregularly" refers to something that is highly inconsistent or erratic. There are several synonyms that can be used to convey this meaning, including haphazardly, randomly, unpredictably, chaotically, unevenly, sporadically, and intermittently. Each of these words carries a slightly different connotation, but all suggest that something is not following a regular or predictable pattern. Whether describing the behavior of a person, the appearance of a landscape, or the performance of a piece of machinery, these words can be used to emphasize the high degree of variation and unevenness that is present.