Fractals are geometrical objects which create a reduced self-sized copy of the object which they originate from. The geometric pattern is repeated at smaller scales, and it is eventually turned into an irregular shape which cannot be measured or represented by classical geometry. Fractals are primarily applied in computer modeling, where they are used for a better understanding of certain structures found in nature.
In fact, fractals came to be a part of natural sciences when it was observed that some nature objects display properties of a fractal - they are complex shapes with self-similarity in their structures. Although a segment of a natural fractal structure may not be perfectly identical with other parts of that structure, it does match closely when put under the microscope.
These geometrical objects can be self-similar when the scale of magnification is changed for one of them. For example, a river and its tributaries may loosely follow a fractal structure, wherein every tributary has its own tributaries. Therefore, it has a similar structure as the river, even though it covers a smaller area.
Other nature structures where you will find self-similar structures are mountain ranges, clouds, crystals, lightning, broccoli, cauliflower, pulmonary vessels, blood vessels, and snow flakes. Other examples in nature include a coastline with numerous peninsulas and inlets, the structure of a galaxy, and the distribution of galaxies in our universe. In economics, the rise and fall can be fractals too, when they are plotted as a function of time. Even within our own bodies, there are instances of fractals, including the branching of the blood vessels, bronchioles, and nerves.
The triadic Koch curve is one of the methods by which a fractal can be constructed. With this method, a straight segment is drawn. Then, it is divided into three identical parts, where the central part is substituted by two similar pieces. Consequently, four segments are created. The same procedure is applied on each of the four segments, and it is repeated for an infinite number of times. The resultant curve creates the distinctive self-similar pattern known as a Koch Curve.
The fractal concept is often used by physicists for analyzing the properties of amorphous solids as well as rough interfaces. It can also be used in the study of the dynamics of turbulence as well as the dynamics of population. In medicine, fractals are deployed to analyze heart rhythm and blood circulation. In computer graphics, compressing a large amount of visual information is rendered effectively by identifying the commonly occurring fractals in that scene, and those fractals are reconstructed to arrive at a shape which closely resembles the original nature scene.
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