In perception research, various models have been designed for the encoding of, for example, visual patterns, in order to predict the human interpretation of such patterns. Each of these encoding models provides a few coding rules to obtain codes for a pattern, each code expressing regularity and hierarchy in that pattern. Some of these models employ the minimum principle which states that the human interpretation of a pattern is reflected by the simplest code for that pattern, ie the simplest code according to a given complexity metric. In this paper a new complexity metric is proposed. This metric is based on a formal analysis of the concept of regularity. Some conclusions of this analysis are sketched. The new metric does not depend on artifacts of the coding rules. It accounts for the amounts of irregularity and hierarchy as represented in a code of a pattern, such that these two amounts can be added to determine the complexity of a code. An experiment is discussed that shows that the new metric performs significantly better than the metrics used previously. In particular, the new metric predicts more local pattern organizations than the old metrics. This implies that various local pattern organizations do not falsify the minimum principle anymore.