And right at the phase transition? In the material world, a given molecule might wind up in the ordered phase or the fluid phase; there would be no way to tell in advance, because order and chaos are so intimately intertwined at the molecular level. In the von Neumann universe, likewise, the Class IV rules might eventually produce a frozen configuration, or they might not. But either way, Langton says, the phase transition at the edge of chaos would correspond to what computer scientists call "undecidable" algorithms. These are the algorithms that might halt very quickly with certain inputs—
