Short sci-fi story about AI creatures that eventually escape into another dimension [duplicate]

Question

Years ago, I read a short story about the creation of an AI species. I believe they were described as crab-like. I remember the creator could speed up their evolution by letting the simulation run. Once they evolved language, the creator would communicate with them. Eventually, they discovered writing and math. After a few more sped-up iterations, they surpass human knowledge and finally find a way to escape safely into another dimension.

I cannot remember the name, and I cannot find it despite my best efforts with Google.

Answer 1

This is Crystal Nights by Greg Egan.

Basically as you've described. An AI researcher is hired by a reclusive billionaire to help generate an artificial intelligence using literal genetic algorithms. Eventually they escape the petri dish into another dimension.

You can read it online on the writer's own site here

Answer 2

You might be thinking about Accelerando by Charles Stross. The book is a series of short stories, originally published separately.

I believe they were described as crab-like.

One of the major entities is a cluster of AIs which originated from brain-scans of the California spiny lobster.

they surpass human knowledge and finally find a way to escape safely into another dimension

The lobsters don't exactly escape into another dimension; rather, they are (initially) used as the "crew" of an otherwise-unmanned deep-space craft. The book continues post-Singularity though with weakly-godlike AIs patterned on them.

The "other dimension" may be the part of the series taking place in a virtual reality pseudo-environment in an alien processing system running over wormholes.