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The three key players in the game of life and evolution

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The five that got it right

No use, distribution or reproduction is permitted which does not comply with these terms. Abstract Cellular automatons and computer simulation games are widely used as heuristic devices in biology, to explore implications and consequences of specific theories. Conway's Game of Life has been widely used for this purpose. This game was designed to explore the evolution of ecological communities.

We apply it to other biological processes, including symbiopoiesis. We show that Conway's organization of rules reflects the epigenetic principle, that genetic action and developmental processes are inseparable dimensions of a single biological system, analogous to the integration processes in symbiopoiesis.

We look for similarities and differences between two epigenetic models, by Turing and Edelman, as they are realized in Game of Life objects.

  1. In fact, it doesn't stabilize until generation 1103. Read the space and follow the instructions.
  2. Red spaces mean you have to stop on the space, even if you have moves left. If we want to model and explain the complexity of dynamic biological systems we need to recognize the importance of the epigenetic dimension, fundamental in constructing biological realities.
  3. Lorenz 1995 and Eckmann and Ruelle 1985 proposed a three dimensional system as fitting this specification. Separate the other cards into four piles.

We show the value of computer simulations to experiment with and propose generalizations of broader scope with novel testable predictions. We use the game to explore issues in symbiopoiesis and evo-devo, where we explore a fractal hypothesis: They provide judgment on the strengths of competing hypotheses, and generate unexpected or unsuspected possibilities for biologists to study and prove empirically.

We show how this crucial function for practicing scientists can be found in the strategic use of versions that are usually dismissed by scientist as trivial and unserious. This purpose explains the interest of this game for biologists, since it explicitly aims to model a basic process in biology, the evolution of ecological communities see Caballero et al.

Yet for heuristic purposes it is equally important to apply it to phenomena which were not part of the original intention. In that way we can test whether the game has a heuristic function, the capacity to develop new explanations which were not envisaged in the initial design.

In the process we can understand better what deeper biological principles are being modeled in this simulation.

Conway's Game of Life

Lorenz 1995 and Eckmann and Ruelle 1985 proposed a three dimensional system as fitting this specification. In this respect he was adding a new requirement for complex biological models like those of Maturana et al. We apply his model in the first place to epigenetic processes, which we understand in a broad sense, to refer to all mechanisms which act on the realizations of genetic action, not just to heritable DNA-modifications such as methylation. Epigenetics is now a broadly accepted aspect of genetics.

In the 1950s and 1960s as proposed by Waddington it was seen as a competitor to genetics. Epigenetics in this context are all those factors involved in the regulation of DNA that do not involve changes in the sequence Waddington, 1962 ; Jablonka and Lamb, 2015.

The information encoded in the DNA of cells is the same for each cell of an organism. All cells and tissues of an organism arise from a primordial cell. Throughout development these acquire identities involving individual differentiation. Thus, we see large divergences between different cell types, which have specific functions. In the development from cells to complete organisms, there are important differences in what we call individuality.

This individuality results from a series of informational factors formed by the genome and the epigenome, which is in feedback with environmental stimuli from the cellular level to the ecosystem. There are many mechanisms implicated in epigenetic regulation. These include the marking of the DNA by various chemical groups that are bonded to the bases of the DNA; genomic imprinting; protein histone modification; regulatory ncRNAs non-codifying RNAs ; epigenetic mark maintenance; environmental effects Inbar-Feigenberg et al.

Environmental factors can alter epigenetic marks, impacting on the development of embryos and also affecting at least the next generation. This transgenerational effect of environmental conditions is a major focus of interest. It is still little-known, but it obviously opens up an interesting path in understanding the relationship of living beings with their environment, and therefore development and evolution Jablonka et al.

If we want to model and explain the complexity of dynamic biological systems we need to recognize the importance of the epigenetic dimension, fundamental in constructing biological realities. In this article we look the three key players in the game of life and evolution at two seminal works in the development of mathematical epigenetic models, connecting them with Game of Life projections in order to develop a generative matrix for thinking about the foundations of epigenetic theory.

Alan Mathison Turing is best known as a father of computing, but his model for morphogenesis 1952often named the Reaction-Diffusion model, has proved an influential mathematical model for epigenetics Turing, 1952.

We look closely at his original proposal, which has been as hard to interpret as it has been influential. We also use a later application of his ideas specifically to biology, the Oster-Murray mechanochemical model Oster et al. As a complementary perspective we use Edelman's concept of topobiology 1988again connected with the Game of Life. GoL was described by Conway as a board game the three key players in the game of life and evolution for zero or one player, but from the beginning it was played out on a computer format, in a program written by Michael Guy and Stephen Bourne.

Conway said that without this format some discoveries about the game would have been difficult to make Gardner, 1970. Conway presented his concept as a board game, to be played with two kinds of counter of different colors, e.

  • There are also many Java implementations of The Game that can be run under in most modern web browsers, though they are usually slower;
  • The F-pentomino stabilizes meaning future iterations are easy to predict after 1,103 iterations;
  • Most games inaccurately portrayed evolution, usually in the same way Spore did — allowing player intervention to save organisms that were unfit for survival;
  • Since there must be three neighbors in order for a cell to come to life, there cannot be a tie;
  • These rules only begin to act after a set of counters has come to exist, in numbers and configurations that come from a decision process that is outside Conway's rules;
  • Taking Your First Turn On your very first turn, you must decide whether you want to begin a career or go to college.

There are three main rules as stated in his description of the game: Every counter with two or three neighboring counters survives for the next generation. Each counter with four or more neighbors dies is removed from overpopulation. Every counter with one neighbor or none dies from isolation. Each empty cell adjacent to exactly three neighbors — no more, no fewer—is a birth cell. A counter is placed on it at the next move Gardner, 1970.

These rules only begin to act after a set of counters has come to exist, in numbers and configurations that come from a decision process that is outside Conway's rules.

In the game they come from the player, making decisions about counters and their positions. In computer versions of the game these decisions are made by algorithms. In biological terms, existential rules correspond to genetic rules. Conway's three spatial rules correspond to epigenetic rules.

As is a property of complex systems, the operation of these rules produces emergent new forms, with properties that are not predictable from the initial conditions.

  • A player could gain 50 points by reaching "Happy Old Age" in the upper-right corner, opposite "Infancy" where one began;
  • After looking at and trying to understand the easier examples, the students can play around with some of the files in this compilation by Jason Summers of popular and look at other interesting patterns;
  • Move ahead the indicated number of spaces;
  • Some cards say Degree Required; if you pick one of these then you must pick again;
  • There is always exactly one generation of evolution between separate players' actions.

These new forms and properties do not involve changes in initial conditions, since the counters are unchanged, but in the emergent forms, the configurations that emerge, and their properties. They produce a wide variety of individual forms from a simple primordial origin Conway identifies three distinctive emergent forms.

Such cycles can be short e. These emergent forms are exciting and remarkable, since oscillation and motion are two properties of living forms that were not part of the content of any of the rules, existential or conditional.