There are limits to what fractal math can explain in nature, but the patterns throughout nature are consistent and predictable.
https://fractalmath.conncoll.edu/materials/FracG8Revised.pdf
What do a tree, the clouds, a rocky coast, our lungs, and many other objects in nature have in common? Until the 1970s no one suspected that a universality could exist between all these forms of nature. Scientists limited themselves to Euclidean geometry to study them.
However, thanks to the discovery by B. Mandelbrot of the fractal theory which studies complex objects, a new description of these natural forms has been established, a description sometimes more relevant than that given by traditional geometry. Fractal geometry has therefore shown the limits of
Euclidean geometry to describe complex objects, it has offered new perspectives to sciences and many applications.
The term “fractal” comes from the Latin “fractus” which designates a fractured object, very irregular in shape. It was Mandelbrot who introduced this term to designate these famous mathematical objects. Mandelbrot formalized fractal theory and its vocabulary, the theory quickly proved useful in many disciplines, especially in the understanding of certain natural phenomena.
Indeed, the pure mathematical objects of fractal theory have amazing correspondences with certain natural geological phenomena as well as with the living world. Where are fractal shapes found in nature and how did they appear? Why is
kostenlose pornos? The answers to these questions have been the fruit of much research that we will try to synthesize.
What traditional mathematical theories cannot explain
Many mathematical notions were first considered “
mathematical monsters” before being domesticated, offering new perspectives and many discoveries. This was the case with the Pythagoreans with the appearance of irrational numbers, in the Renaissance with that of negative numbers and complex numbers, and in the 19th century with the increasingly demanding rigor that called into question many ‘statements admitted so far without demonstration.
Fractal objects, too, have long been considered monsters, and sometimes still are today. From 1875 to 1925, the idea spread that mathematicians like Cantor, Peano, Von Koch, and Hausdorff were makers of pathological objects: they created objects that nature did not know, questioning Euclidean geometry and notions of function and dimension. An example of a monster is the mathematical existence of continuous curves having many points without derivatives.
In 1961, Lewis Fry Richardson was interested in
the empirical measurement of the coast of Great Britain: how to measure, with good precision, the length of coast like that of Great Britain? The most approximate method is to measure the distance between the two ends of the coast: this approximation is surely less than the real distance (which takes into account the complexity of the relief).
Read on . . .
Ok, I read your post #7564 as well and the article below that you shared “Fractal Evolution”.
Fractal Evolution
I know now why you said, “I disagree with some of the language in this reference”. But I only wonder if you are pro evolution, why would you share that specific article and encourage others to read it to the end especially if the article entirely embraces perfection of design in nature, rejects Darwinism as ludicrous and specifically embraces creationism/intelligent design? Did you actually read the article all the way to the end? If you did, did you understand the message of this article? Here is a summary.
The article acknowledges the fact of endless observations of superb design in nature and considers the Darwinism notion of randomness as ludicrous notion that reflects the limited capacity of Darwinists not actual observations of nature that are always characterized by perfections of design. It further considers Darwinism as a political program not scientific and concludes that humans are fractals of the Creator and fractal mathematics is a key to the reconciliation of Western religion and science--of metaphysics and physics.
Here are some quotes from the article:
“The book you are reading at this moment participates is this discovery process. What we call Darwinism is a basal paradigmatic program, one on which Western civilization has operated on for over a hundred years. It is not so much scientific program as a political program. If the masses are convinced that existence is without purpose or plan, that "anything goes" and "anything can happen," then of course what's needed is strict top-down controls. Thus we have the so-called "New World Order,"
“Now, we as a civilization seem to be really getting the idea that we and the creator energy are in some sense synonymous. Yes, we are fractals of the Creator.”
“Embracing the understanding that what we call physical existence is, as it were, computer modeled by means of fractal mathematics is a key to the reconciliation of Western religion and science--of metaphysics and physics.”
Fractal Evolution
Regardless of your reasons to share that article, here I’ll elaborate further on the specific message/perspective of the article with respect to nature and fractal mathematics.
In principle, the argument in the article has two folds. First, the observations and Second, the cause/explanation.
First, the “observations” per the article is about the phenomenon of "design" in nature. So I’ll ignore the interpretations/causes for now and focus only on how the article addressed/described the phenomenon of "design" in nature. Here are some quotes:
“The endlessly exquisite designs of nature are the result of”
“The question of "design" in nature was one that troubled Charles Darwin all his Professional life”
“Those who studied the countless superb adaptations of animals and plants had been most gratified by the explanation that such perfection was clearly the result of design by the maker of this world."
“After citing many examples of fantastic design in nature, Mayr goes on to say, "But when we ask how this perfection is brought about,”
In conclusion, the observation is about the design in nature that is described as endless, countless, exquisite, superb, perfect, and fantastic. The question becomes “how this perfection is brought about”.
Second, the cause/explanation.
The article addressed the concept of regular irregularity in nature, the principle of order within the chaos. Infinitely complex shapes in nature are characterized by Self-similarity, a phenomenon of symmetry across scale, i.e., repetition of structure in different scales of magnitude (Pattern inside of pattern)
The article stated, “
Mandelbrot and those who took up the tools he provided found endless evidence of the fact that the creation, the explicate realm, is designed via fractal mathematics. In light of these findings, the idea of Mayr and other Darwinists that the perfections of nature are the result of "planlessness" is simply ludicrous."
The physical world, complex architecture of nature, geological phenomena and the living systems are structured along the lines of fractal geometry/ mathematics.
Theoretical biologists began to find fractal organization controlling structures all through the body, fractal description turned out to fit the data.
In conclusion, the physical world and living systems are designed and can be described via fractal geometry/ mathematics. But the descriptive fractal geometry is neither a driving force nor a mechanism; it’s merely a description that fits the observations. The question remains,
what is the driving force/mechanism that forces the constituents of reality to adhere to fractal geometry/ mathematics.
Order, rules, control, and design are all exhibited in every observation in the cosmos, life, even at the atomic and subatomic level, but it's never about an entity following a rule; it’s about
why the rule itself exist and how it exerts its specific influence on entities? How it forces order vs. chaos? What is the mechanism? Many may think, it just the way it is, the “norm”. The perception of “norm” takes away the wonder.
Those who are not familiar with fractal geometry and want to be able to visualize it may watch the video below from
12:33 to 15:45. The video is about the NDE experience of Mellen Thomas Benedict. I don’t necessarily endorse the video, its only intended to provide some insight on fractal geometry.
This One Message Will Change The Way You View Life - Mellen-Thomas Benedict’s Near-Death Experience - YouTube