"Geometry is the science of measuring with precision. It subjugated the surface in the compass and measured the dimensions of the visible universe. It is the systematic method which has led man from truth to infinity. For this reason, the study of this science must be made the object of special study [...]'
Fractal geometry is essentially the geometry of self-similar structures, objects, forms, shapes and even processes of evolution in time. By self-similarity we mean that the structure remains invariant to a scaling invariance transformation. In other words, Fractal geometry is the geometry of symmetry of self-similarity, which, combined with the amazing advances in computer technology, has become the ideal medium for the observation and study of complexity. By giving the computer the command "the formula to be repeated many times", images with organic characteristics and an art-like quality are created, allowing fractals to demonstrate that true chaos is opposed to the simulation created by the repetition of a mathematical formula.
Everyday experience brings people into contact with numerous geometric forms, which are immediately perceived. For their study and understanding, however, their representation is necessary. However, none of the known and accepted geometric structures, such as the ideal forms of Euclidean Geometry or those of non-Euclidean Geometry (in Gauss's terminology), or the radical conception of Riemann, who imagined a space "curved", with arbitrary dimension, has the ability to accurately describe the perpetual motion and sloshing of waves breaking on the shore, the random geometric shapes in the branches of trees, the sudden bursts of wind, the snowflakes, or even the cellular tumors, the muscle tissues and the blood vessel system in the human body, as Fractal geometry indirectly serves human health and the human being himself is essentially a composition of fractal shapes! The most prominent example is the structure of the lungs, in which the lung tree itself is an unadulterated fractal in its structure and function, but also the circulatory system and the brain and heart.
Thus, although a complicated mathematical concept, Fractal Geometry has essential application to every human aspect of vital value. Nature itself that surrounds us is consisted of fractals, which is why mathematicians, health experts, physicists, geologists, architects, engineers and many others study it with considerable enthusiasm.
The clouds of the sky, leaves, forests, flowers, snowflakes, river networks, mountains, as well as galaxies and other space entities present the structure of fractals, through which we perceive not only the magic and beauty of nature and the planet that is our home, but ultimately the beauty of the mathematics they enclose, captivating in the smallest degree even the most mathematically distant people.
But let us go further and imagine the complete modeling of the center of the human spirit, the brain, and the existential implications it will bring about in approaching, studying and decoding human consciousness or even.... the soul!
"Geometry is the foundation of positive science [...]" and "[...] the study of the sciences is necessary, because all of them can become sources of virtue".
It is 'necessary to know the essence of phenomena in order to solve the enigma of life'.
Fractals are a way to "see" infinity!