def logpofr_old(r):
    """
    Returns the nat. logarithm of a fit to the probability of finding
    a zone of density contrast r in a Poisson particle simulation
    """
    
    # 2D
    #p = -2.6*(r-1.)
    # 3D
    p = -5.12*(r-1) - 0.8*(r-1)**2.8
    
    return p