This paper proposes a methodology for designing a class of algorithms for computing functions in dynamic distributed systems in which communication channels and processes may cease functioning temporarily or permanently. Communication and computing may be interrupted by an adversary or by environmental factors such as noise and power loss. The set of processes may be partitioned into subsets that cannot communicate with each other; algorithms in which all such subsets behave in a similar fashion, regardless of size and identities of processes, are called self-similar algorithms. Algorithms adapt to changing conditions, speeding up or slowing down depending on the resources available. The paper presents necessary and sufficient conditions for the application of a self-similar strategy. Self-similar algorithms are developed for several problems by applying the methodology.