Yesterday (1.5.2019) there was a lecture at LUCIS, given by Christian Muller: "The Evolution of Islamic Legal Thought". Approaching the conclusion, he switched his PowerPoint presentation to Mandelbrot's fractal, wishing to illustrate his idea: that Sharia law is a kind of iterative system that gives a changing pattern at the early iterations (the beginnings of Islamic history), only to stabilise later on. The subsequent iterations, as it is intensely re-iterated even today, provoke only minor differences in that general, stabilised pattern.
Certainly, Mandelbrot is rather a badly chosen example; he would need, I suppose, a simpler fractal; Mondelbrot's is one of those rather complex, and its main feature is the appearance of small bonhommes, similar to the overall pattern, as its border gets complicated. This has no visible analogy with the formation of the Sharia law system, as it was presented. A Sierpinski's triangle might be a better illustration (as all the finesse remains in the pre-established boundaries of the Revelation - if it's what we want to accentuate). Perhaps also not a fractal, but an attractor is the mathematical object that would better correspond to Muller's idea.
Be that as it may, I find this conclusion brilliant, and it puts me on the track of an interesting experiment. Is it possible to treat certain areas of human intellectual actions, based on changing, yet relatively stable parameters (sort of holy rules of traditional activity) as the basis of autopoiesis that leads to emergence of patterns with discernible qualities and characteristics in the large scale? The multiplicity of single interpretative acts that makes the history of Islamic legal thought would be an excellent example, that might be put in comparison with other cultural systems based on similar iteration.