Evolution of Autopoiesis and Multicellularity in the Game of Life.

Recently we introduced a model of symbiosis, Model-S, based on the evolution of seed patterns in Conway's Game of Life. In the model, the fitness of a seed pattern is measured by one-on-one competitions in the Immigration Game, a two-player variation of the Game of Life. Our previous article showed that Model-S can serve as a highly abstract, simplified model of biological life: (1) The initial seed pattern is analogous to a genome. (2) The changes as the game runs are analogous to the development of the phenome. (3) Tournament selection in Model-S is analogous to natural selection in biology. (4) The Immigration Game in Model-S is analogous to competition in biology. (5) The first three layers in Model-S are analogous to biological reproduction. (6) The fusion of seed patterns in Model-S is analogous to symbiosis. The current article takes this analogy two steps further: (7) Autopoietic structures in the Game of Life (still lifes, oscillators, and spaceships-collectively known as ashes) are analogous to cells in biology. (8) The seed patterns in the Game of Life give rise to multiple, diverse, cooperating autopoietic structures, analogous to multicellular biological life. We use the apgsearch software (Ash Pattern Generator Search), developed by Adam Goucher for the study of ashes, to analyze autopoiesis and multicellularity in Model-S. We find that the fitness of evolved seed patterns in Model-S is highly correlated with the diversity and quantity of multicellular autopoietic structures.

Measuring Behavioral Similarity of Cellular Automata.

Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic cellular automata, a family with 262,144 members. Many of these automata may deserve as much attention as the Game of Life, if not more. The challenge we address here is to provide a structure for organizing this large family, to make it easier to find interesting automata, and to understand the relations between automata. Packard and Wolfram (1985) divided the family into four classes, based on the observed behaviors of the rules. Eppstein (2010) proposed an alternative four-class system, based on the forms of the rules. Instead of a class-based organization, we propose a continuous high-dimensional vector space, where each automaton is represented by a point in the space. The distance between two automata in this space corresponds to the differences in their behavioral characteristics. Nearest neighbors in the space have similar behaviors. This space should make it easier for researchers to see the structure of the family of semi-totalistic rules and to find the hidden gems in the family.

Symbiosis Promotes Fitness Improvements in the Game of Life.

We present a computational simulation of evolving entities that includes symbiosis with shifting levels of selection. Evolution by natural selection shifts from the level of the original entities to the level of the new symbiotic entity. In the simulation, the fitness of an entity is measured by a series of one-on-one competitions in the Immigration Game, a two-player variation of Conway's Game of Life. Mutation, reproduction, and symbiosis are implemented as operations that are external to the Immigration Game. Because these operations are external to the game, we can freely manipulate the operations and observe the effects of the manipulations. The simulation is composed of four layers, each layer building on the previous layer. The first layer implements a simple form of asexual reproduction, the second layer introduces a more sophisticated form of asexual reproduction, the third layer adds sexual reproduction, and the fourth layer adds symbiosis. The experiments show that a small amount of symbiosis, added to the other layers, significantly increases the fitness of the population. We suggest that the model may provide new insights into symbiosis in biological and cultural evolution.

The natural selection of words: Finding the features of fitness.

We introduce a dataset for studying the evolution of words, constructed from WordNet and the Google Books Ngram Corpus. The dataset tracks the evolution of 4,000 synonym sets (synsets), containing 9,000 English words, from 1800 AD to 2000 AD. We present a supervised learning algorithm that is able to predict the future leader of a synset: the word in the synset that will have the highest frequency. The algorithm uses features based on a word's length, the characters in the word, and the historical frequencies of the word. It can predict change of leadership (including the identity of the new leader) fifty years in the future, with an F-score considerably above random guessing. Analysis of the learned models provides insight into the causes of change in the leader of a synset. The algorithm confirms observations linguists have made, such as the trend to replace the -ise suffix with -ize, the rivalry between the -ity and -ness suffixes, and the struggle between economy (shorter words are easier to remember and to write) and clarity (longer words are more distinctive and less likely to be confused with one another). The results indicate that integration of the Google Books Ngram Corpus with WordNet has significant potential for improving our understanding of how language evolves.

Self-replication and self-assembly for manufacturing.

It has been argued that a central objective of nanotechnology is to make products inexpensively, and that self-replication is an effective approach to very low-cost manufacturing. The research presented here is intended to be a step towards this vision. We describe a computational simulation of nanoscale machines floating in a virtual liquid. The machines can bond together to form strands (chains) that self-replicate and self-assemble into user-specified meshes. There are four types of machines, and the sequence of machine types in a strand determines the shape of the mesh they will build. A strand may be in an unfolded state, in which the bonds are straight, or in a folded state, in which the bond angles depend on the types of machines. By choosing the sequence of machine types in a strand, the user can specify a variety of polygonal shapes. A simulation typically begins with an initial unfolded seed strand in a soup of unbonded machines. The seed strand replicates by bonding with free machines in the soup. The child strands fold into the encoded polygonal shape, and then the polygons drift together and bond to form a mesh. We demonstrate that a variety of polygonal meshes can be manufactured in the simulation, by simply changing the sequence of machine types in the seed.