The Times says, "Dr. Mandelbrot coined the term 'fractal' to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature." Mandelbrot's discoveries profoundly influenced mathematics and the sciences and numerous disciplines beyond.
In our most recently published paper ("In Search Of The Logic Of Judaism: From Talmudic Chaos To Halakhic Linearity") we end with a section called, "Fractal conclusions." That brief discussion leverages Mandelbrot's concepts to illuminate a discipline far afield from anything he worked on:
We have examined above first some common views of scholars concerning the idea of the halakhah in Judaism. We then explained why their methods failed to account for the main philological and historical evidence regarding the term from the Talmudic texts. Then we suggested a heuristic explanation that the logic of the Talmud defies linearity can be productively discussed using chaos theory. Perhaps even more intuitively, we shall conclude that the Talmud may be compared metaphorically to fractals. A fractal image emerges when a single equation is applied to some initial condition and the outcome is a colored point of complex patterns. We have the basic components for making an imaginary fractal out of the texts of rabbinic Judaism: miẓwot, middot, truths, and values, applied in different contexts by various authorities leading to differing colored and complex results (see note below).In a note we explain that our colleague, technology Professor Kevin Dooley endorses an expanded metaphor:
We close with some certainty that the chaotic Talmud needs to be better imagined before one can understand the details of the logic of its more linear offshoots, the tomes of halakhic reasoning. Last, we believe that this more rigorous theoretical exploration and more detailed philological textual analysis of our cultural constructs of both Talmudic thought and halakhic reasoning advances our admiration for the great contributions of the past and helps us find the greatest ultimate theoretical meaning of all – to know more intimately the intentions of the one who first brought order out of primeval chaos and utter void.
If you look at one of the fractal images, the way it emerges is that a single ‘equation’ is applied to some ‘initial condition,’ and the outcome is recorded as some colored dot. Metaphorically, we have some simple set of rules, truths, commandments, values, being applied in different contexts, leading to different results. So yes, there are some small set of ‘rules’ which hold throughout, which from your discussion appears to be what the ‘LAWS’ were trying to capture. But as these laws are applied in different contexts, different interpretations emerge which are context dependent, which appears to be what the Talmud is about. So it would seem that in a strong metaphorical sense, the Talmud is fractal. (Systems which self-organize often have these fractal characteristics).