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Collatz Conjecture (Ulam Conjecture/Kakutani’s problem/Thwaites conjecture/Hasse’s algorithm/Syracuse problem/3n+1 Conjecture) Even: ÷2 Odd: ×3 + 1 ×3 + 1 3 ×3 + 1 ÷2 10 5 ÷2 16 8 ÷2 ÷2 ÷2 4 2 ×3 + 1 1 ×3 + 1 3 ×3 + 1 ÷2 10 5 ÷2 16 8 ÷2 ÷2 ÷2 4 2 ×3 + 1 1 Is there a number that doesn’t end up at 1? 266 = 295 147 905 179 352 825 856 “Mathematics is not yet ripe enough for such questions.” - Paul Erdős Coral Simulation Fractal <20 steps tree