One of the main problems of evolutionary algorithms is the convergence of the population to local minima. In this paper, we explore techniques that can avoid this problem by encouraging a diverse behavior of the agents through a shared reward system. The rewards are randomly distributed in the environment, and the agents are only rewarded for collecting them first. This leads to an emergence of a novel behavior of the agents. We introduce our approach to the maze problem and compare it to the previously proposed solution, denoted as Novelty Search (Lehman and Stanley, 2011a). We find that our solution leads to an improved performance while being significantly simpler. Building on that, we generalize the problem and apply our approach to a more advanced set of tasks, Atari Games, where we observe a similar performance quality with much less computational power needed.

The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph showing which elementary cellular automata can be emulated by which and show that certain chaotic automata are the only ones that cannot emulate any automata non-trivially. Finally, we use the emulation notion to suggest a novel definition of chaos that we believe is suitable for discrete computational systems. We believe our work can help design parallel computational systems that are Turing-complete and also computationally efficient.

An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge, here we introduce Combinatory Chemistry, an Algorithmic Artificial Chemistry based on a minimalistic computational paradigm named Combinatory Logic. The dynamics of this system comprise very few rules, it is initialized with an elementary tabula rasa state, and features conservation laws replicating natural resource constraints. Our experiments show that a single run of this dynamical system with no external intervention discovers a wide range of emergent patterns. All these structures rely on acquiring basic constituents from the environment and decomposing them in a process that is remarkably similar to biological metabolisms. These patterns include autopoietic structures that maintain their organisation, recursive ones that grow in linear chains or binary-branching trees, and most notably, patterns able to reproduce themselves, duplicating their number at each generation.

Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for enough computational capacity. Understanding complex computations happening in cellular automata and other systems capable of emergence poses many challenges, especially in large-scale systems. We propose methods for coarse-graining cellular automata based on frequency analysis of cell states, clustering and autoencoders. These innovative techniques facilitate the discovery of large-scale structure formation and complexity analysis in those systems. They emphasize interesting behaviors in elementary cellular automata while filtering out background patterns. Moreover, our methods reduce large 2D automata to smaller sizes and enable identifying systems that behave interestingly at multiple scales.

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method distinguishes between different asymptotic behaviors of a system's average computation time before entering a loop. When applied to elementary cellular automata, we obtain classification results, which correlate very well with Wolfram's manual classification. Further, we use it to classify 2D cellular automata to show that our technique can easily be applied to more complex models of computation. We believe this classification method can help to develop systems, in which complex structures emerge.