GoKawiilWolfram Research offers prizes for unsolved questions about Rule 30 cellular automaton
Rule 30 is one of 256 simple cellular automata built from a single logic rule applied repeatedly to rows of black and white squares, first studied systematically by Stephen Wolfram in the early 1980s. Despite its simplicity, the automaton's central column of cells has never been proven to either repeat or avoid repeating, even though statistical tests show it behaving like a fair coin toss. The pattern was long used to generate random integers in Mathematica and has been applied decoratively, including on buildings at Cambridge.