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Essay / Fractals: how they are self-similar - 664
Fractals are everywhere around us, in our lungs, our kidneys, our blood vessels, our plants, in the clouds, in the trees, in the landscape and even in our heartbeat. . But what exactly is a fractal? Simply put, a fractal is something that exhibits self-similarity. This means that when you zoom in or out, the object looks the same. Fractals are all around us in nature. Fractals are found in clouds, in trees and in our lungs, livers and veins. A team of people went to a protected forest, cut down some trees (with permission of course!) and took measurements of the trees. Based on these measurements, they were able to see that there were consistent repeating patterns in where the branches separated and how thick the branches were. They found that this extended not just to individual trees, but to the entire forest. Classical mathematics started from the basic assumption that everything is regular and has smooth edges. Until the arrival of Benoit Mandelbrot. He saw mathematical equations as pictures in his head. After teaching for a time in France, he left to work at IBM. A problem occurred while transmitting data over the telephone lines and we decided to plot the noise data. The graph was the same whether the time interval was a minute, an hour, a day, or even a week. Benoit Mandelbrot was one of the first to experiment with fractals. He created a set of numbers now known as the Mandelbrot set by using a computer to run an equation millions of times and turned the numbers into points on the graph. He discovered that when you zoomed in on the series after plotting it, the images created repeated themselves. He later wrote a book on the appearance of fractals in nature. A programmer named Loren Carpenter came across......the middle of a paper......has small bumps or grooves that can be created. using fractals. Fractals can also be used in animation. As previously stated, it is possible to create mountains as well as entire planets using fractals. Fractals were first introduced to the film industry in Star Trek II: The Wrath of Khan, where the entire flyby planet was created using fractals. In a scene from the new Star Wars movie; Anakin and Obi Wan face off inside an active volcano. The lava in the scene was created using fractals. The artist added swirls to the 3D model of the initial lava spout and reduced them. They repeated the process over and over again, layering each one until the entire background was fractal swirls. Fractals have today become an important element in the creation of video games. It can be used to create terrains, forests, entire worlds, textures and special effects..