![]() In fact, it has even been proven that Conway’s Life can be used to build a universal ( Turing-complete) computer - albeit a very inefficient one. There are many more interesting examples out there. (There are four versions, each mirror images, which move in the four diagonal directions.)Īn excellent example of emergent complexity is the “R-Pentomino”: a set of five cells which explodes in a burst of activity, firing off several gliders until finally becoming stable over a thousand generations later(!) Shortly after it was invented, the “glider” was discovered - which can move diagonally. These are somewhat interesting - but the beauty of Conway’s Life is in the more complex behaviors it can produce: …but a diagonal row of cells “anchored” at both ends remains stable. Three cells in a row will oscillate between horizontal and vertical configurations - becoming a “blinker.”Ī diagonal row of cells will evaporate from each end… Each live cell has three live neighbors no empty cell has more than two - therefore, no cells ever die or are born. Here are some examples:Ī “block” of four squares will remain exactly as it is - a classic example of a “still life”. The most interesting ones, though, can drift away across the plane, grow without bound, or play out in a chaotic manner for hundreds or thousands of generations before becoming stable. Some configurations quickly die out others quickly evolve into stable “still life” configurations. These two simple rules lead to all sorts of interesting behavior. If a “dead” (or “empty”) cell has exactly three neighbors, it becomes “alive” in the next generation.Otherwise, it “dies” (potentially to be reborn again later). If a “live” cell has exactly two or three neighbors, it remains “alive” in the next generation.John Conway in 1970, Life is a specific cellular automaton: a set of rules for updating the states (“alive” or “dead”) of a rectangular grid of cells (Conway apparently did some early investigations using a checkerboard.) Starting from a given “seed” configuration, the following two simple rules are repeatedly applied (to all of the cells at once): Another example is Conway’s Game of Life.ĭiscovered / invented by Dr. Fractals such as the Mandelbrot Set are a good example of this. Often, very simple systems can lead to complex behavior. One of the more interesting topics in math (for me, anyway) is emergent complexity. The whole idea is to show the fun side of math!) Don’t worry, though there won’t be a quiz. (This is the first of a planned series of articles on interesting topics in mathematics.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |