Pseudo-number generation compared to Blum-Micali A few years ago I made a pseudo-random number generator to use in a monte carlo simulation for a lecture in my University.

My instructor ask me why I did that generator instead of using C equivalent rand.

The algorithm is $x_{n+1} = e^{x_n + k} \mod 1$ using float point values with $K$ big enough to contain a complete cycle inside $\epsilon$ (a very small value).

Yesterday I find another PRNG using a similar formula: Blum-Micali algorithm

$x_{n+1} = g^{x_n} \mod p$

The answers are... could my algorithm be based on the Blum-Micali one?

Could my algorithm contain the Blum-Micali properties?

Thanks in advance.
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.