Rule 30: one black cell

Rule 30 is a simple cellular automaton discovered by Stephen Wolfram in the 1980s that generates seemingly random patterns from a basic mathematical rule applied to rows of black and white squares. Despite its simplicity, the center column of Rule 30 passes randomness tests, making it a cornerstone example of how deterministic rules can produce unpredictable behavior—a key insight in Wolfram's "A New Kind of Science." Wolfram has offered $30,000 in prizes for proving three properties about this center column (whether it's non-periodic, fair, and computationally irreducible), questions that remain unsolved after seven years despite a billion computed cells.