Resonant Spacetime Hypothesis 2.0

    if (log_periodic) {  

      double phase = 2 * M_PI * log(n + 1) / log(beta);  

K      A[n] = amplitude_0 * exp(-pow(log(n + 1) - mu, 2) / (2 * sigma_sq)) * std::polar(1.0, phase);  

    } else {  

      A[n] = gaussian_rand() * sqrt(Pk[n]);  

    }  

  }  

  return A;  

}  

```  

MPI Parallel FFT