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Game of life python code9/27/2023 The simplest grid would be one-dimensional: a line of cells.įigure 7.16: A Textile Cone Snail (Conus textile), Cod Hole, Great Barrier Reef, Australia, 7 August 2005. What are the three key elements of a CA?ġ) Grid. Let’s build Wolfram’s elementary CA from scratch. To understand Wolfram’s elementary CA, we should ask ourselves the question: “What is the simplest cellular automaton we can imagine?” What’s exciting about this question and its answer is that even with the simplest CA imaginable, we will see the properties of complex systems at work. The examples in this chapter will begin with a simulation of Wolfram’s work. This chapter will barely scratch the surface of the theories Wolfram outlines (we will focus on the code implementation) so if the examples provided spark your curiosity, you’ll find plenty more to read about in his book. Available in its entirety for free online, Wolfram’s book discusses how CA are not simply neat tricks, but are relevant to the study of biology, chemistry, physics, and all branches of science. Perhaps the most significant scientific (and lengthy) work studying cellular automata arrived in 2002: Stephen Wolfram’s 1,280-page A New Kind of Science. (Incidentally, von Neumann’s cells had twenty-nine possible states.) Von Neumann’s work in self-replication and CA is conceptually similar to what is probably the most famous cellular automaton: the “Game of Life,” which we will discuss in detail in section 7.3. This is essentially the process of a CA that exhibits behavior similar to biological reproduction and evolution. Now consider a set of simple rules that would allow that pattern to create copies of itself on that grid. Consider the design of a robot as a pattern on a grid of cells (think of filling in some squares on a piece of graph paper). Once we see some examples of CA visualized, it’ll be clear how one might imagine modeling crystal growth the robots idea is perhaps less obvious. That’s right, robots that build copies of themselves. Ulam was studying the growth of crystals and von Neumann was imagining a world of self-replicating robots. The development of cellular automata systems is typically attributed to Stanisław Ulam and John von Neumann, who were both researchers at the Los Alamos National Laboratory in New Mexico in the 1940s. In this context, cellular automata make a great first step in building a system of many objects that have varying states over time.Ī cellular automaton is a model of a system of “cell” objects with the following characteristics. We’ve alluded to the possibility that these entities can change over time (for example, the weights of steering “desires” can vary), but we haven’t fully put this into practice. In Chapters 1 through 6, our objects (mover, particle, vehicle, boid) generally existed in only one “state.” They might have moved around with advanced behaviors and physics, but ultimately they remained the same type of object over the course of their digital lifetime. To simplify our lives, we’ll also refer to cellular automata as “CA.” Our code examples will simulate just one-a cellular automaton, singular. 7.1 What Is a Cellular Automaton?įirst, let’s get one thing straight. Working with such simple elements will help us understand more of the details behind how complex systems work, and we’ll also be able to elaborate on some programming techniques that we can apply to code-based projects. This bit is going to be called a cell and its value (0 or 1) will be called its state. No longer are the individual elements going to be members of a physics world instead we will build a system out of the simplest digital element possible, a single bit. Oddly, we are going to take some steps backward and simplify the elements of our system. This entire chapter is going to be dedicated to building another complex system simulation in Processing. We briefly stated the core principles behind complex systems: more than the sum of its parts, a complex system is a system of elements, operating in parallel, with short-range relationships that as a whole exhibit emergent behavior. In the previous chapter, we encountered our first Processing example of a complex system: flocking. In fact, the rest of the book will mostly focus on systems and algorithms (albeit ones that we can, should, and will apply to moving bodies). In this chapter, we’re going to take a break from talking about vectors and motion. Martin Gardner, Scientific American (October 1970) It is possible to work with pencil and graph paper but it is much easier, particularly for beginners, to use counters and a board.” “To play life you must have a fairly large checkerboard and a plentiful supply of flat counters of two colors.
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