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2.5 Game of Life
Discussion
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Cells on a matrix are called 2D Cellular Automata (2D CA). The best known version is Conway’s Game of Life.
Instructions
1. Play the The Game of Life.
2. Upon completion, answer the questions below.
a. If you have more black squares or white squares, do you get more emergent patterns? Why or why not?
b. Compare and contrast the Game of Life with life. Do the patterns you see reflect patterns you would expect to see in real living systems? Why or why not?
3. Read and respond to answers shared by others. -
1. If you have more white squares, you get an emergent pattern. This is because when there are a lot of black squares, they all immediately die from overcrowding.
2. The rules set for the Game of Life are very similar to a simplification of normal life, however the end scenario is different. There are “stable” configurations in the Gam of Life in which the game board does not change or keep repeating in a finite time period. I could not find an analog to this in real life.
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Rachana,
There’s actual an entire field of modeling- system dynamics modeling- that’s all about finding equilibrium (or “stable”) states, even biological systems. You don’t seem them as much at the level of individual organisms, but they definitely do show up at the ecosystem level. Trophic cascades are a great example- an ecosystem can have two or more stable states or configurations, depending on what higher level consumers (grazers, predators, etc) are present, and will flip into the alternate state if some of those consumers are added or removed.
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The rules in Game of Life are an oversimplification of real life. Many biological factors affect the increase or decrease and concentration or dispersion patterns of populations of living organism. One will need a multi-factor model, not just a model based on a single factor of how many adjacent neighbors one living organism has.
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There is some ideal state of a specific starting ratio of black squares to white square, as well as a specific way in which those squares are arranged, at which you get the most emergent patterns. On a function modeling population growth, I would assume that this state would correspond to the point of inflection. From the model, it seems that you get more emergent patterns with more white squares than black squares. However, with too many white squares, the population dwindles to zero from underpopulation. I feel that the most important aspect of this simulation is to find the ideal state that generates the most emergent patterns, which depends both on the starting ratio of black squares to white square and where those squares initially lie.
As Johann said, the game of life is an oversimplification of life. There are many more aspects that effect population dynamics. However, I think as a model to explain the general concept of how populations grow, shrink, and eventually either die out or reach some equilibrium state, the game of life is extremely effective. There are more complicated reasons for why populations change than those presented in the game of life, but the game of life is a beautiful mathematical illustration of the general concept of population dynamics.
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