This article lists fourteen open problems in artificial life, each of which is a grand challenge requiring a major advance on a fundamental issue for its solution. Each problem is briefly explained, and, where deemed helpful, some promising paths to its solution are indicated.

Evolution of genetic codes is studied as change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states of a cell allows for a choice of enzymes, and this choice is later fixed genetically through evolution. To demonstrate this theory, a dynamical systems model consisting of the concentrations of metabolites, enzymes, amino acyl tRNA synthetase, and tRNA–amino acid complexes in a cell is introduced and studied numerically. It is shown that the biochemical states of cells are differentiated by cell-cell interactions, and each differentiated type starts to use a different synthetase. Through the mutation of genes, this difference in the genetic code is amplified and stabilized. The relevance of this theory to the evolution of non-universal genetic code in mitochondria is suggested. The present theory is based on our recent theory of isologous symbiotic speciation, which is briefly reviewed. According to the theory, phenotypes of organisms are first differentiated into distinct types through the interaction and developmental dynamics, even though they have identical genotypes; later, with mutation in the genotype, the genotype also differentiates into discrete types, while maintaining the “symbiotic” relationship between the types. Relevance of the theory to natural as well as artificial evolution is discussed.

By introducing a dynamical system model of a multicellular system, it is shown that an organism with a variety of differentiated cell types and a complex pattern emerges through cell-cell interactions even without postulating any elaborate control mechanism. Such an organism is found to maintain a larger growth speed as an ensemble, by achieving a cooperative use of resources, than do simple homogeneous cells, which behave “selfishly.” This suggests that the emergence of multicellular organisms with complex organization is a necessity in evolution. According to our theoretical model, there initially appear multipotent stem cells, which undergo stochastic differentiation to other cell types. With development and differentiation, both the chemical diversity and the complexity of intra-cellular dynamics are decreased, as a general consequence of our system. Robustness of the developmental process is also confirmed.

To understand an architecture of a living system, “Tile Automaton” is introduced as an abstract model of chemical reaction of molecules scattered over a space. The model consists of tiles of various shapes that stand for molecules. The chemical reaction, induced by the collisions of tiles, is represented by the change of the tile shapes. The rules for reaction are deterministic, and the evolution of the system strongly depends on mutual spatial relationship among tiles. The evolution often leads to self-organization of a “factory,” a set of tiles that produces tiles continuously and keeps its structure. Several interesting phenomena, such as a deformation or a division of a factory, are also observed. It is proposed that the formation of the factory is due to the interference between different aspects of tiles—the shape and the motion. The concept of “entanglement” is introduced as a mechanism of living systems.

The origin of multicellular organisms and the mechanism of development in cell societies are studied by choosing a model with intracellular biochemical dynamics allowing for oscillations, cell–cell interaction through diffusive chemicals on a two-dimensional grid, and state-dependent cell adhesion. Cells differentiate due to a dynamical instability, as described by our “isologous diversification” theory. A fixed spatial pattern of differentiated cells emerges, where spatial information is sustained by cell–cell interactions. This pattern is robust against perturbations. With an adequate cell adhesion force, active cells are released that form the seed of a new generation of multicellular organisms, accompanied by death of the original multicellular unit as a halting state. It is shown that the emergence of multicellular organisms with differentiation, regulation, and life cycle is not an accidental event, but a natural consequence in a system of replicating cells with growth.

A nonzero-sum three-person coalition game is presented to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and mutations. Two types of differentiation emerge initially: a biased one to classes and a temporal one to change their roles for coalition. Rules to change the hands are self-organized in a society through evolution. The coevolution of diversity and complexity of strategies and interactions (or communications) are found at later stages of the simulation. Relevance of our results to the biological society is briefly discussed.

The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of identical chaotic elements, globally coupled each to the other, is briefly reviewed. The clustering is extended to nonlinear dynamics on hypercubic lattices, which enables us to construct a self-organizing genetic algorithm. A mechanism of maintenance of diversity, “homeochaos,” is given in an ecological system with interaction among many species. Homeochaos provides a dynamic stability sustained by high-dimensional weak chaos. A novel mechanism of cell differentiation is presented, based on dynamic clustering. Here, a new concept—“open chaos”—is proposed for the instability in a dynamical system with growing degrees of freedom. It is suggested that studies based on interacting chaotic elements can replace both top-down and bottom-up approaches.