fractal theory

A very intriguing concept I came across is that of fractals - a term newly coined by mathematician Benoit Mandelbrot in the late 20th century, which is defined as a complex geometrical pattern which is surprisingly formed by the continuous repetition of simple self-similar sub-patterns. A few special observations about fractals include : self-similarity (i.e the geometric structure of the pattern remains consistent when viewed across different scales) and ordered complexity or randomness (i.e. the ability to generate complexity and randomness by just repeating simple patterns again and again across different scales). What amused me about fractals is how it could be analogized to serve as a possible explanation for the nature of reality. Stephen Wolfram - a computer scientist and physicist, who authored a book called ‘A New Kind of Science’, theorizes that reality is essentially a computing process where certain simple rules are just continuously being repeated with time which ultimately gives rise to the ordered complexity of reality which we experience presently, much similar to a fractal. By this explanation, reality is essentially a forward branching tree with highly increasing complexity where each sub-branching keeps following simple rules of updation ultimately emerging as an immensely complex system as a whole with ordered randomness where the final outcome is not really predictable in spite of the inherent order by virtue of its complexity. When we observe reality, we come across a variety of diverse and asymmetrical outcomes in the form of matter, species, geography, ideologies etc. But among these diverse outcomes, we observe commonalities that still exist in the form of what appears to be the laws of physics which appears to be the order in the chaotic randomness of reality. As mentioned earlier, a fractal as a whole is a complex pattern but if we zoom in sufficiently at any point on the fractal, we can always observe self-similar sub-patterns. Parallels of self-similarity and ordered randomness can be observed in nature in many areas : diverse organisms while complex end up having the similar biological architecture in the form DNA code being executed by ribosomes to produce proteins resulting in functioning organs, the prefrontal cortex which is the arguably most sophisticated constituent responsible for intelligence is also fractal of sorts where simple pattern modules (PRM) are repeated over and over resulting in complex intelligence, the possibility of scientific method where we are able to formulate mathematical equations to predict physical phenomenon which work consistently across the world enabling all of the engineering we see in the present. This begs many questions : why do the laws of physics exist? why does the scientific method happen to work? why do so many diverse outcomes exist the way they do while always being bounded by certain universal rules? This creates a very interesting viewpoint about what could be the purpose of reality where reality could ultimately just be an experiment being run which was programmed at the dawn of time with a simple set of rules presumably rules likely equivalent to the laws of physics (which appear to be fine-tuned to make existence possible) allowed to continuously iterate and branch out with time like a set complex fractals in the form of recursive physical computational programs to produce what we presently see as our reality continuously proliferating the self-similar sub-branches of the fractal-like physical computational programs across differents scales and dimensions. This viewpoint serves as a good explanation for the nature of reality by accounting for its unpredictable complexity while also accounting for the inherent natural order. Organisms, human intelligence, consciousness and technology are ultimately different incremental and unplanned outcomes of the program produced at different iterations with time with each increasing iteration allowing for more complex computing i.e. further branching of the fractals of reality leading to produce more diverse and random outcomes within the experiment while being bounded by a certain order.