Cosmos Automaton: A Deterministic Fractal Automaton Generating Primes

This paper introduces the "Cosmos Automaton" (CA), a deterministic fractal automaton that generates prime numbers through symbolic operations rather than direct primality testing. By treating the sequence of natural numbers as a dynamic process, we show that primality emerges from the constructive interference of "pulse trains" (periodic symbolic words). We demonstrate that the CA’s structures are isomorphic to the set of natural numbers and that its evolutionary steps correspond to arithmetic progressions. This approach provides a visual and algorithmic bridge between automata and the distribution of primes, leading to a definition of primality based on geometric expansion. This provides a new algorithmic perspective on the structure of primes.