A new pretraining approach called Self-Play Pretraining with Zero Data enables language models to generate their own training data by casting synthetic data generation as a search over computable structures, inspired by Solomonoff induction. Two models learn in tandem—a generator proposes programs interpreted by a universal Turing machine while a learner predicts the resulting byte sequences—creating an adaptive curriculum where the learner improves predictably with compute. The method achieves measurable zero-shot transfer to natural data without any exposure to it during training.