A major theoretical problem in the phenomenon of emergence, in which new properties appear as a result of the interaction of familiar elements, is to explain the origin of those new properties. If they are not inherent in the elements themselves, where do they come from?
If they are inherent in these elements, how can this be reconciled with< atomic theories in which simpler elements combine to produce more complex ones? A further and connected problem is to predict, for a new and previously untried interaction, what particular emergent properties will appear.
In this paper an approach to these problems is suggested in terms of a model of self-similarity, in which the emergent properties are inherent in the interacting elements themselves. This leads to a view of the elements of an interaction as being complex, like the "monads" of Gottfried Leibniz, rather than simple, as in atomic theories.
The model is developed with particular reference to the emergence of different properties from the same elements depending on their mode of combination. According to this theory the probability of the emergence of new properties is a function of the sequence of operations upon the monads involved in the inducing process and emergent properties are seen as being highly sequence-dependent.
This approach is discussed with reference to a number of examples, including the efficiency of chemical reactions, the character of social interactions and the morphology of the developing organism. Its implications for atomic theories of ontology and ontogeny are discussed and a theory of monadic structure is tentatively proposed.