What’s more perplexing to experts is that despite the simple, deterministic, rules used to build the automata up, the results never converge. Remarkably, it turns into the pattern at the top of the page if you run it for enough iterations. The elementary CAs are often referred to as “rules” (reason why at ). Note that all the cells in the row evolve in parallel. For example, row 2 column 2 is a “-” because there is a “-” “-” “-” above it, as described in the 2nd to last rule of the “Rule” above. Each cell from the 2nd row onwards is computed based on its own shape and the shape of its neighbors above according to the key on the top.The CA will do drastically different things based on the initial conditions, but typically the same sorts of shapes will appear. The values of the top row could be anything: they could be random, or just have 1 star in the middle, as we have here. The top row of cells is a hand-chosen initial configuration. First, we start at the top row of cells.The command to generate the CA is from the library I provide. All this being said, they’re easiest to understand by example:Ĩ evolutions of rule 30, starting with one star in the middle. Each cell in the grid evolves based on its neighbors and some rule.Įlementary CAs are visualized by drawing a row of cells, then evolving that row according to a rule, and displaying the evolved row below its predecessor. A cell is a particular location on a grid with a value, like a cell on a spreadsheet you’d see in Microsoft Excel. All the code is on Github, so you can read through it:Ĭellular Automata Basics: The Elementary CAsĬAs are computational models that are typically represented by a grid with values (cells). I didn’t like many of the ones I was encountering elsewhere on the internet because I felt they weren’t beginner friendly enough. I’ve also written a library in Python to generate the CAs which I use throughout the post. You won’t need to know coding to read this post, but for more technical readers I provide endnotes and Github repos. In this post I’ll go over some famous CAs and their properties, focusing on the “elementary” cellular automata, and the famous “Game of Life”. If you’re interested in the philosophical implications of cellular automata, check out my post here.Ĭellular Automata (CA) are simultaneously one of the simplest and most fascinating ideas I’ve ever encountered. Rule 30 was discovered by Stephan Wolfram in ’83. The famous rule 30 capable of generating pseudo-random numbers from simple/deterministic rules.
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