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Wolfram Language (Mathematica), 71 bytes

StringRiffle[CellularAutomaton[30,{{1},0},31]/.{1->"1",0->"."},"\n",""]

Try it online! A code snippet that produces a string.

Gotta have the OG in the house. Note the 30 in this code is precisely why this cellular automaton is called Rule 30! See the CellularAutomaton documentation for how it encodes the rule of evolution.