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.

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.

Life turns fifty

Mention to computer scientists, gliders, glider guns, birth and death rules and they smile remembering their efforts to study societal life. October marked the 50th anniversary of the publication of John Conway's game of Life in Martin Garner's Mathematical Games column [1], For the lay person with no knowledge of Life, it's difficulty to imagine how popular a single person game with only a single move (i.e. setting the initial conditions) could be.

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.

Segmentation of Brain MRI with Tumor by Image Overlapping using Cellular Automata

In order to improve the health care reach, we need efficient and fast computer aided simulation processes or algorithms. When some change is found in pathological reports and biomedical quantities, the person is susceptible to diseases. If the diseases are detected earlier then there can be increase in the rate of mortality. Tumor is one such disease which has been seen to be one of the most fatal for human beings. Detecting and removing tumor is big challenge for medical practitioners. Medical image processing can be used through cellular automata has proven to be one of the fast and reliable method for detection of tumor cells. To study the capabilities of medical science CA’s are being used extensively, as they are useful in studying the selfreproducing biological systems. Purpose: This paper presents an algorithm for segmentation of MRI image through cellular automata, using Conway’s Game of Life. A new approach is being used in this paper, first the image is converted into gray level image. Then edge detection is done for this image using Game of Life. This edge detected image is overlapped with the gray scale image to get the resulted segmented image as an output. Materials and Methods: In order to run the proposed algorithm MATLAB2019b is used and the images are obtained. Results: Algorithm was used on different MRI’s and the results were taken.