Pseudo-number generation compared to Blum-Micali
No, your algorithm is fundamentally different.  The resemblance is purely superficial.  The Blum-Micali generator is based on integers modulo a large prime number, and leverages deep number theoretic ideas.  Yours is based on the fractional part of real numbers (hence the "mod 1"), and is not based on number theory and not related to Blum-Micali.  Blum-Micali is cryptographically secure.  Your scheme seems unlikely to be.