A fractal algorithm shows prime number patterning

We present a novel mathematical machine with a novel fractal algorithm for modeling the distribution of prime numbers and gaps. This framework leverages three fractal processes with deterministic rules to construct six walksets. Walksets An and APn act as collectors, Bn and BPn determine prime or composite, Cn starts with all natural numbers and CPn contains the fractal process with always periodic patterns. Primes and gaps arise as emergent phenomena within this rule-based system – proving that this Ansatz holds for all prime numbers and gaps. We call the machine “Synchronous Factory Automaton” SFA. It was implemented in Java.