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"id": "https://mathstodon.xyz/users/mrdk/statuses/110833323942042537",
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"published": "2023-08-04T20:51:51Z",
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"content": "<p>Number-conserving cellular automata can be thought as simulating particle systems, like grains of sand or cars in a street.</p><p>I have just placed a text about one-dimensional number-conserving cellular automata into the arXiv (<a href=\"https://arxiv.org/abs/2308.00060\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/2308.00060</span><span class=\"invisible\"></span></a>). It is a kind of sequel to an earlier paper, in which I had derived a general construction scheme for all such automata. But a lot of things are still unknown, and the theory of such automata looks quite interesting. In my new paper I prove some new theorems, describe how to simulate the automata on a computer and how to find interesting rules, and I show images of a few rules I have found this way. Comments are welcome!</p><p><a href=\"https://mathstodon.xyz/tags/CellularAutomata\" class=\"mention hashtag\" rel=\"tag\">#<span>CellularAutomata</span></a> <a href=\"https://mathstodon.xyz/tags/NumberConservation\" class=\"mention hashtag\" rel=\"tag\">#<span>NumberConservation</span></a></p>",
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"en": "<p>Number-conserving cellular automata can be thought as simulating particle systems, like grains of sand or cars in a street.</p><p>I have just placed a text about one-dimensional number-conserving cellular automata into the arXiv (<a href=\"https://arxiv.org/abs/2308.00060\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/2308.00060</span><span class=\"invisible\"></span></a>). It is a kind of sequel to an earlier paper, in which I had derived a general construction scheme for all such automata. But a lot of things are still unknown, and the theory of such automata looks quite interesting. In my new paper I prove some new theorems, describe how to simulate the automata on a computer and how to find interesting rules, and I show images of a few rules I have found this way. Comments are welcome!</p><p><a href=\"https://mathstodon.xyz/tags/CellularAutomata\" class=\"mention hashtag\" rel=\"tag\">#<span>CellularAutomata</span></a> <a href=\"https://mathstodon.xyz/tags/NumberConservation\" class=\"mention hashtag\" rel=\"tag\">#<span>NumberConservation</span></a></p>"
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"updated": "2023-08-04T20:53:02Z",
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"name": "A number-conserving cellular automaton at low density. Time goes up, the darker a square is, the more particles it contains. One mainly sees particles coming from the left and particles coming from the right, with interactions when their paths cross. The image appears on Figure 1.3 of the paper.",
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