The geometry of the universe
The geometry of the universe
The geometry of the fractal universe. Geometry that lives in the midst of nature's own diversity. What does a fractal look like with a map of a continent or an explanation of a river? I repeatedly break the black triangle in the figure into numerous small triangles. I keep breaking. Fractal can be found. Its special name is Sier-pinski Gasket. Fractal is nothing more than a repetitive reflection of a basic single structure. When a fractal is formed by the exact replacement of the basic structure, this feature is called Linear Self-Similarity. However, the fractals that work behind the phenomena of nature have never been so Self-Similar. For example, the foliage of a plant or the bank of a river. So what is the reason behind this diversity of natural fractals?
As we know, the relationship between two or more signs can be expressed by an equation. We also know from Descartes that each equation points to a specific path of transmission and can be expressed in graphs. For example, y ^ 2 = 4ax expresses the equation of the hyperbola. If one rides a bicycle in an elliptical path, then this phenomenon i.e. the motion of the bicycle can be expressed by the equation y ^ 2 = 4ax. Similarly, behind every phenomenon of nature there is a work of more complex equations.
The matter can be shown in a slightly broader background. Kepler's equation indicates the motion of the planets around the Sun. Kepler's formula is able to make accurate predictions over a long period of time about the orbits of a planet in a solar system made up of one star and one planet. But what will be the course of the planet after 50 million years? If an extra star were added to the structure of the solar system, what would be the orbit of the planets in the solar system of twin stars after only five million years? It is then extremely difficult to make accurate predictions. Almost impossible.
Assuming, x = ky explains a natural phenomenon. Here x and y are related to each other proportional constant ‘k’. As the value of x increases or decreases, the value of y increases or decreases in proportion to k. But if the value of constant k from time to time is affected by another quantity c then the relationship between x and y cannot be said to be simple proportional. Then it is difficult to make precise inferences about the graphs of x and y. Can this be imagined with the population growth-equation of a region!
Diversity on the canvas of nature is here. The fractals of the phenomena of nature are therefore unequal, irregular, random. And this indeterminacy is the basis of Chaos theory. Chaos is the uncertainty that changes over time in the course of nature. So there is an asymmetry in the restoration of the basic structure. Again, some rhythms can be observed in the case of transition from symmetry to asymmetry or return to symmetry. And its overall manifestation occurs in the variegation of the fractal. In a word, fractal comes from Euclid's simple linear world to explain nature in its own way.
So guess where the chaos is? There is action on the leaves floating in the current of water, constantly changing its direction. There may be some specific uncertainties in the growth and decline of insects, animals or human populations. But after a certain period of time it is often possible to know the amount of total uncertainty. Then the accuracy of future predictions increases, so the Chaos theory is being applied to weather forecasting. He is also being sought behind a "whirlwind" of liquid or gas flows. Chaotic Unpredictability is also found in Number Theory, a branch of pure mathematics. So does this theory work in human society? Regular irregularities! How much of this irregularity in the universe at God's will?
