Jonathan,
Math! - Its so long ago, that it now resides only in my 'imaginary' brain cells.
'Your paper is to be an exciting exploration of bouncing between what is 'possible to know' and 'what is beyond reckoning'. '.
Perhaps the (interesting) Mandelbrot Set and Planck scale are guides specifically for mathematicians. You are seeking converges or condenses, but shouldn't 'expands' be a third alternative. You say 'one area of Physics for which the Mandelbrot Set provides useful insights is the study of gravity'. However, if you see things as a cosmologist might, the options go beyond the 2 or 3 possibilities, even beyond reckoning'
I suggest that all things can be contemplated as nothing is absolute. Everything under investigation has parts. There is a field between known and 'beyond reckoning' with varying probabilities throughout. 'We reside in a middle ground between fixed realities and variable conditions, over which we have no control.'
Gravity, my interest, seems to reveal that what we know can be just the opposite of how it is. 'When crafting a unifying theory of Physics, a problem is that Relativity time is flexible, while in QM it is absolute'. Supposedly the need to reconcile these theories is the main incentive for quantum gravity theorists and the reason so many worthy approaches to the problem have been spawned. None work well since simple options are ignored. 'There is a growing knowledge gap because, as things become more complex; more things cannot be known, more facts cannot be proven, and more proofs can never be tested.' Seems all are upside down.
The sheer volume of collected data distorted knowledge, as it must be stored and then searched through later hoping to find the bits of information (buried deep within) that contain what we want to know.' 'So time spent is the ultimate barrier to knowledge, since it is the one limitation we can never hope to overcome.'
Best wishes Jonathan.
Paul Schroeder