In Paper #2 in the "Selected Papers" section of
www.amherst.edu/~rloldershaw the scaling constant Lambda, and the self-similarity constant D, are derived using the physical parameters of the Solar System, the physical parameters of atoms, and knowledge atomic and stellar mass distributions.
The initial values are accurate at the 95% level, which has been sufficient to subject the discrete self-similar paradigm to a large battery of retrodictive tests.
The website section "Successful Retrodictions + Predictions" currently lists 33 examples of reasonably unique agreement with the observed properties of nature. Four more will be added to the list soon. You cannot get this level of agreement by chance or any amount of fudging [without
many ad hoc "fixes"]. Discrete Scale Realtivity has never required ad hoc "fixes", mythological particles, colors, strings, "asymptotic freedom", etc., etc., etc.
In principle, one can derive more accurate values of Lambda and D if one can identify any pair of analogues on two neighboring Scales and take ratios of their radii and masses. Stellar masses still have a problematic amount of uncertainty, but observational techniques keep improving. But I'm not a perfectionist; the 95% level is fine for my purposes.
One should look to nature for guidance. The abstract mathematical approach has generated far more smoke and Ptolemaic junk, like "string theory", than light.
The Mandelbrot Set is a truly exquisite entity, but it is a child's toy compared to the infinitely infinite self-similarity of nature. Luckily for us, the principles underlying the whole thing are remarkably few and simple, as is the case with the M-Set. Discrete Scale Invariance is the one principle that is currently most under-appreciated.
RLO