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"I love that computer science has made mathematics into something like an experimental science. I was never all that good at proving things, but I love doing computer experiments."
- Rudy Rucker

Brood Assembly  
  Artificially intelligent computers that can replicate themselves.  

What can you do when your city needs artificially intelligent computers to guide it?

He [Mayor Amalfi] was saying to Frad: "The arrangements with the machinery are cumbersome, but not difficult in principle. We can lend you our Brood assembly until she replicates herself; then you reset the daughter machine, feed her scrap and out come City Fathers to the number that you'll need - probably about a third as many as we carry, and it'll take maybe ten years. You can use the time feeding them data, because in the beginning they'll be idiots except for the computation function.
From Cities in Flight, by James Blish.
Published by Avon in 1957
Additional resources -

Readers will recognize the idea of self-reproducing automata, which John von Neumann wrote about in 1948 in a lecture called "General and Logical Theory of Automata".

You can read an even earlier treatment of the idea in the 1941 short story The Mechanical Mice, by Eric Frank Russell (writing as Maurice A. Hugi). See the entry for robot mother.

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Additional resources:
  More Ideas and Technology from Cities in Flight
  More Ideas and Technology by James Blish
  Tech news articles related to Cities in Flight
  Tech news articles related to works by James Blish

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