Cosmos Automaton

This paper introduces the Cosmos Automaton (CA), a new type of automaton. It is generating fractal patterns based on prime number distribution and prime gaps. Unlike the classical Sieve of Eratosthenes, which requires a finite upper bound, the CA is round based, starting with a step and terminating each round with completing the step and thus can run infinitely in theoretical operation. We demonstrate that this mechanism resolves the “infinite loop” problem of static sieves and constructs the fractal structure of prime distributions bottom-up via additive operations. Three fractal processes are applied to the symbol tape and the fractal dimension is calculated. In order to show the efficiency and feasibility of the proposed algorithm, we apply the Chinese Remainder Theorem to the automaton’s state transitions to demonstrate the infinitude of twin primes. We show via mathematical induction that the population of twin prime templates grows geometrically with each step, ensuring that they occur within the automaton’s stability zone – which is free of the parity problem – infinitely many times. As we do not use any densities, the lumpiness of twin primes does not matter.