Heredity, Complexity and Surprise: Embedded Self-Replication and Evolution in CA Chris Salzberg 1,2 and Hiroki Sayama 1 1 Dept. of Human Communication, University of Electro-Communications, Japan 2 Graduate School of Arts and Sciences, University of Tokyo, Japan Abstract. This paper reviews the history of embedded, evolvable self- replicating structures implemented as cellular automata systems. We relate recent advances in this field to the concept of the evolutionary growth of complexity, a term introduced by McMullin to describe the central idea contained in von Neumann’s self-reproducing automata the- ory. We show that conditions for such growth are in principle satisfied by universal constructors, yet that in practice much simpler replicators may satisfy scaled-down — yet equally relevant — versions thereof. Examples of such evolvable self-replicators are described and discussed, and future challenges identified. 1 Introduction In recent decades, the study of embedded self-replicating structures in cellular automata has developed into one of the main themes of research in Artificial Life[31, 32]. A common goal motivates such research: to extract the fundamen- tal organizing principles that govern real-world biological phenomena (and, in a wider sense, life as we know it[13]) from an abstraction of their driving biophys- ical processes. Central among such processes is self-replication in its variety of forms. The eminent mathematician John von Neumann was the first to suggest that essential features of such biological self-replication, with its many degrees of freedom and complex kinematics, could be usefully represented in a discrete cel- lular space with uniform local rules[41]. His seminal self-reproducing automata theory, which he situated “in the intermediate area between logic, communica- tion theory and physiology”[41, p.204], set the stage for future research in ar- tificial self-replication[16] and remains among the defining achievements of this field[17]. Following von Neumann’s work of the late 1940s and early 1950s, research on CA-based self-replicators split into a number of major trends. Among these, the majority are efforts to implement regulated behavior (universal construc- tion[8, 9, 20, 38, 40], self-replication[5, 12, 14, 18, 22, 34], self-inspection[11], func- tionality[7, 19, 37]) manually introduced to satisfy pre-defined goals of the de- signer. Such goal-oriented design is important for resolving theoretical problems (bounds and limitations on self-replicating structures) and for direct applica- tion (computation, problem-solving, nanotechnology), yet does little to address the fundamental issue that shaped von Neumann’s original theory. This issue centers on the vague and intuitive concept of “complication”[41, p.78], roughly measured in terms of the number of elementary parts of a machine or organism.