![]() The control question is: Can this goal be accomplished? The cells outside the top-left corner will be initialized at random, and you do not get to see what their initial configuration is when you decide on the initial configuration for the top-left corner. ![]() Now suppose that I give you control of the initial on/off configuration of a region of size 10 20 by 10 20 in the top-left corner of this grid, and set you the goal of configuring things in that region so that after, say, 10 60 time steps the state of the whole grid will resemble, as closely as possible, a giant smiley face. Suppose that we are working with an instance of Life with a very large grid, say 10 30 rows by 10 30 columns. Take a look at this awesome video of a Universal Turing Machine operating within Life. It is possible to build logic gates and combine them together into a computer that can simulate any Turing machine, all by setting up a particular elaborate pattern of "on" and "off" cells that evolve over time according to the simple rules above. It turns out that these simple rules are rich enough to permit patterns that perform arbitrary computation. Over time, the cells switch between on and off according to a simple set of rules:Ī cell that is "on" and has fewer than two neighbors that are "on" switches to "off" at the next time stepĪ cell that is "on" and has greater than three neighbors that are "on" switches to "off" at the next time stepĪn cell that is "off" and has exactly three neighbors that are "on" switches to "on" at the next time step In Conway’s Game Life, which I will now refer to as just "Life", there is a two-dimensional grid of cells where each cell is either on or off. ![]() In this post I am going to discuss a celular autonoma known as Conway’s Game of Life: I propose the AI hypothesis, which is that any pattern that solves the control question does so, essentially, by being an AI. I argue that the permissibility or impermissibility of AI is a deep property of our physics. This question is then connected to questions of agency and AI, since one way to answer this question in the positive is by constructing an AI within Conway’s Game of Life. This post asks whether it is possible, in Conway’s Game of Life, to arrange for a certain game state to arise after a certain number of steps given control only of a small region of the initial game state. I welcome financial support to make further posts like this possible.Įpistemic status: I have been thinking about these ideas for years but still have not clarified them to my satisfaction. It's a game that highlights the beauty of mathematical patterns and invites players to marvel at the interplay of order and chaos in a virtual world.Financial status: This is independent research. While Conway's Game of Life here on SilverGames doesn't involve direct player interaction, it captivates with its simplicity, elegance, and ability to simulate complex behaviors. It's a game of exploration and observation, as players witness the intricate and sometimes unexpected patterns that emerge from simple rules. In Conway's Game of Life, players can observe the evolution of different patterns and experiment with initial configurations to see how they affect the outcome. The game is often used as a tool for studying complex systems and exploring emergent behavior. These rules give rise to fascinating patterns and behaviors that unfold over time. The rules of the game are simple: based on the status of neighboring cells, each cell in the grid will either survive, die, or be born in the next generation. The game is played on a grid of cells, and each cell can be either alive or dead. It is a zero-player game, meaning that the evolution of the game is determined solely by its initial configuration. Conway's Game of Life is a classic cellular automaton and simulation game created by mathematician John Horton Conway.
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