Think about every animated movie you've ever seen, and not only just animated movies, but movies with any computerized special effects. These effects are made possible by fractals! Up until the late seventies, animated movies were made by multiple paintings to create the appearance of movement. But that all changed when Loren Carpenter, a computer scientist working for Boeing Company came across and began to use Mandelbrot's text "Fractals: Form Chance, and Dimension." He used fractals to generate mountain landscapes to aid in the modeling and design of airplanes. He did this by starting with basic triangles as mountains and then would fragment those triangles repeated times and it would make the mountains look more realistic (Jersey & Schwarz, 2011). Carpenter created the first fully "fractally generated" movie called "Vol Libre" and his work became revolutionary in the movie making industry.

Watch Vol Libre

Later on, he went to work for Pixar and the algorithms he used are still used today, after his retirement (Loren Carpenter: Biography, 2015).

Up until Fractals came along, we could only use mathematical modeling with manmade things, such as buildings and architecture, finances and money, etc.. We use Euclidean, hyperbolic, or elliptic geometries to represent these things. But when it came to natural occurrences, the outcomes were too chaotic for anyone to model mathematically. For example, it would be impossible to mathematically model a coastline with only basic geometric figures because clouds are so irregular and form abnormal shapes. It was believed that up until now, nature is simply not mathematical. But with the development and research of fractals, we have found that nature is mathematical, it just is a different type of mathematics, a different type of geometry. We call this new type of mathematics Fractal geometry (Jersey & Schwarz, 2011).

Some applications of fractals that might surprise you are in the fashion industry, in telecommunication, and in the medical world. When fractals became well known, clothing designers began to use fractals to create intricate clothing designs that would be difficult to come up with without computer generations. The use of fractals in telecommunication also has a very large effect on anybody who owns a cell phone! For example, if an antennae wire is bent down into a fractal form, it takes up less space and it receives a wider range of frequencies than a regular antenna. These are now used in cell phones and this is why we no longer have bulky antennas on our cell phones! There are also a lot of applications of fractals in the medical world. Doctors and scientists are using fractal images to help detect cancerous tumors or heart disease sooner (Jersey & Schwarz, 2011).

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