Phi is featured in poetry, music, and great works of visual art, such as Leonardo da Vinci’s “Mona Lisa” and Salvador Dali’s “The Sacrament of the Last Supper.” Some psychologists believe the golden ratio is the most aesthetically pleasing proportion to the human mind, and followers of Pythagoras believed it revealed the hand of God. As a critical concept in mathematics and physics, it made possible the construction of pentagrams, the Egyptian pyramids, and the Roman Parthenon. In the natural world, it appears in mollusk shells, sunflower florets, crystals, and galaxies.
In it, Livio says that Euclid first described phi more than 2,000 years ago. Mario Livio’s book, ” The Golden Ratio: PHI, the world’s most amazing number,” explains the role of phi in human history. The golden ratio is the most irrational number (in up to 20,000 decimals, there is no trace of repeating patterns), but it creates beauty and order in art and natural world phenomena. Fractal mathematics is one of the greatest achievements of the human mind in the digital age. Fractal geometry describes chaotic transition. Euclidian geometry assumes that structures exist only in whole dimensions (1, 2, 3), but fractal geometry allows us to explain the fractional dimensions that exist in the real world (e.g., a snowflake’s dimension is 4/3). In contrast, Euclidian geometry is based on the assumption that surfaces are smooth (planes have only two dimensions). The most surprising quality of fractals is that they are created by repeating basic operational rules which signifies a deep simplicity at the core of this complex universe.įractal mathematics is geometry of the real world, which has rough or irregular surfaces. Even though we see chaos on the surface, at deeper levels we observe that the elements are creating an emerging order of self-similar patterns, where in different scales they display the same degree of order. The result of this plot reveals self-similar patterns in which any magnified part looks just like the larger section from which it was taken. With the help of a computer, we can divide the chaotic zone into much smaller increments and plot the values. Then we reach a zone where the results provide chaotic values without any traceable pattern. Now, if we analyze the values that we obtained at each iteration, we may see patterns where the values are diverging, converging, or constant. If we take a nonlinear function and assume initial values for constants and variables for the first round of iteration, on each round we will get a value that we will feed back into the system. I propose that the fractal dimension of the Golden Ratio could contain this pattern of information therefore, I will briefly explain fractal geometry and the golden ratio.įractal geometry is the geometry of chaos. The living universe is made of cognitive energy that inherently contains a pattern of information which makes it capable of organizing itself into self-organizing nonlinear networks.
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