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I'm looking for a short story about an ocean planet where there are huge mats of algae and no other life. The algae appears dumb but on a cellular level it's running a simulation of another world, and life is evolving in the sim. Some of the life seems to be self aware.

I hope this is accurate, it's been years since I read it. I think I read this in either Asimov's or one of those big anthology books like The Year's Best Science Fiction.

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I believe this is "Wang's Carpets" (isfdb entry) by Greg Egan, a story that formed the basis for the later novel Diaspora.

It was published in the New Legends anthology edited by Greg Bear.

Human consciousness is now running in software, and have been travelling the universe seeking other life. They find a waterworld with large "carpets" moving slowly through the ocean. The humans realise that the carpets are actually running a simulation through their growth, and there may be sentient beings within the simulation.

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    Fantastic, thank you! I'm pretty sure this is it, and I get to read a novel now :D – Rebecca Hartstein Oct 23 at 1:03
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    I just finished Diaspora. Wang's carpets was one of the many mind blowing concepts in the novel. They're made of complex carbohydrates, IIRC, and are based on Wang Tiles. In the 60s Wang showed that they are turing complete, and can thus execute any computation. – Bridgeburners Oct 23 at 12:50
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    If I recall correctly, the carpet-growth calculation wasn't deduced to necessarily be a simulation per se, but rather just a sign of deliberation. That is, maybe it's simulating sentient beings, or maybe the growth is the sentience itself. But that's all a nitpick and timbp's answer is correct in all the important parts; it's a great story! – Ti Strga Oct 23 at 21:52
  • Answer copied over to reddit.com/r/scifi/comments/dlq9wa/… where this was cross-posted, just to link them together. :) – FuzzyBoots Oct 24 at 12:50
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    FWIW, time inside a CA (cellular automaton) world would run very slowly compared to the outside world: computations inside a CA tend to be slow. Patterns that do a specific computation (eg calculating Fibonacci numbers in binary) aren't too bad, but if you need a "programmable" pattern then it can easily take a huge number of CA generations per step in the computation. Eg, the Gemini spaceship takes 33,699,586 generations to rebuild itself. – PM 2Ring Oct 24 at 16:00

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