Topic > Fractals: How They Are Self-Similar - 664

Fractals are everywhere around us, in our lungs, kidneys, blood vessels, plants, clouds, trees, landscape, and even in our heartbeats. But what exactly is a fractal? In simple terms a fractal is something that has self-similarity. This means that when you zoom in and out the object appears the same. Fractals are everywhere around us in nature. Fractals are in the clouds, in the trees and in our lungs, liver 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 could see that there were consistent repetitive patterns of where the branches split and the thickness of the branches. They saw that this extended not just to individual trees, but to the entire forest. Classical mathematics was based on the basic assumption that everything is smooth and has smooth edges. That was until Benoit Mandelbrot came along. He saw mathematical equations as images in his head. After teaching for a time in France, he went to work for IBM. There was a problem with data transmission on telephone lines and it was decided to plot the noise data. The graph was the same regardless of whether the time frame was a minute, an hour, a day, or even a week. Benoit Mandelbrot was one of the first to begin experimenting 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 transformed the numbers into points on the graph. He found that when he zoomed in on the series after it had been traced, the images created repeated themselves. He later wrote a book on the appearance of fractals in nature. A programmer named Loren Carpenter came across... in the center of the paper... there are little 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 and even entire planets using fractals. Fractals were first introduced to the film industry in Star Trek II: The Wrath of Khan, where the entire planet they flew over 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 flow and shrunk them. They repeated the process over and over, each layering on top of each other until the entire background was composed of fractal swirls. Fractals have become an important part of video game creation today. It can be used to create terrain, forests, entire worlds, textures and special effects.