An actively stabilized random number generator includes a random number generator and a feedback controller. The random number generator includes a chaotic physical circuit realizing an iterated function. The iterated function is configured to produce a trajectory of iterates and has an operating parameter β and a desired Markov operating point. A binary bit converter has a symbol function configured to produce binary symbols from the trajectory of iterates and a maximal kneading sequence. The feedback controller is configured to observe the maximal kneading sequence within the trajectory of iterates and adjust the operating parameter to the desired Markov operating point.