The universe is a huge fractal
A bit of an "apple man" philosophy
“Mathematics is the alphabet that helps
God described the universe. "(Galileo Galilei)
Is the Universe a Fractal?
Even if there are now much more impressive fractals than the Mandelbrot set (e.g. the so-called Mandelbulbs), it is still the original 2D fractals of the Mandelbrot set that fascinate me the most, because they most clearly express how the most complex images can emerge from a simple mathematical iteration. With the more modern types of fractal graphics, too much "artificially" has been added to me, so that the actual "artist", the mathematics - the principle inherent in the universe - takes too much of a back seat. With the Mandelbrot set, it is not the person who designs all these shapes, but these are the automatic result of an extremely simple calculation (more about the exact mathematical background on the page Painting by Numbers). Only the color is determined by the human being, since numbers don't have any color; I still find this to be a "legitimate" intervention, comparable, for example, with dyeing techniques when using a microscope or coloring the impressive images of the Hubble space telescope. The structures that can be seen, on the other hand, are completely unchanged and unaffected by human intervention.
That from such a simple and boring looking formula like Zn + 1 = Zn² + C such organic forms can arise, which can have an extremely aesthetic effect on a human observer, seems to me as a "mathematical layman" almost like a "miracle", which led me to the question of a possible deeper meaning of mathematical principles for "The life, the universe and all the rest" led: Already in my first attempts with "apple man" graphics on the C64 around 1989 I had given appropriate considerations. The English-language Fractal Forum also has an area for fractal philosophy with interesting topics, e.g. The fractal experience.
Who knows, maybe the entire universe including us humans and all living beings in it is one huge fractal ... In the Mandelbrot crowd, it is the edge areas between diverging and converging forces that contain the interesting, chaotic structures. In the universe it is the area between absolute emptiness and densest mass (black holes) in which the interesting structures with galaxies, planetary systems and biological life exist. As with the mathematical fractal, the structure of this "intermediate area" becomes more and more complex and finely detailed the further you go into depth. All structures repeat themselves (self-similarity) - from the galaxies, which are orbited by planetary systems, to suns, which are orbited by planets, to atomic nuclei, which are "clouded over" by electrons, and this probably continues in the subatomic area away. So is the world we see the "ordered chaos" in the narrow border area between two opposing forces?
Just as in the Mandelbrot set all visible structures are connected with each other, it could perhaps also be in the universe: Everything is connected and interacts with each other. This does not only seem to apply to celestial bodies that influence each other e.g. through gravitation, but also occurs in the subatomic area as so-called quantum entanglement. Even human consciousness is not isolated from that of other people - even across space and time: There are indications that consciousness exists independently of a biological body and that the brain is only a filter / converter for a "non-local" consciousness (see on YouTube the lecture Nonlocal Consciousness by the cardiologist Pim van Lommel, who deals with near-death experiences of resuscitated patients).
In my research for answers to the question of whether the computer-generated fractals (especially the fringes of the Mandelbrot set) might not be more than mere mathematical curiosities - whether there might be a universal principle behind them - I also went to the website encountered by Gabi Müller. The physicist and former alternative practitioner has developed a theory according to which (to put it very simply) everything that exists consists of fractal eddies of energy. As a "non-physicist" I cannot judge this reality model with regard to its plausibility, but it definitely sounds very interesting and inspiring.
With the two-dimensional representation of the Mandelbrot set, we may only get a tiny glimpse into a fundamental law of nature that stands "behind mathematics" ...
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