Fractal Geometry








Fractal geometry is very important to the twenty-first century. Fractal geometry helps in medical research, designed chips in cell phones, animates movies, and is being applied to more and more concepts daily.


Movie Animations/ Effects

Before people knew about fractal geometry animated movies were made by hand. People would draw a character, and draw him in a new position, and then another. The result would be like a flipbook. When animations came out they were really pathetic looking and hard to make.


A man named Loren Carpenter was working for Boeing airlines when the company decided to animate planes flying. Carpenter wanted the planes to fly over mountains, but he had no way of doing that with the computer graphics. That was when he learned about fractal geometry and how it described nature. He decided to use fractal geometry’s concepts that to make mountains on his computer.


First Carpenter would draw a triangle. Then he would take that triangle and cut it into four triangles, and on each of the other triangles he would cut that into four, and so on. Soon he could make a realistic mountain range for a plane to fly through. Carpenter then moved on to make entire computer sequences for the movie Star Trek, which was the first Hollywood film to use an entirely computer generated sequence.




Video Data

Before fractal geometry video software had to memorize image after image in order to play a film. Software that uses fractal properties helped make video files take up less data space. It did this by finding pixel squares that matched other pixel squares. It would memorize just those set of pixels and their placement on the screen. Now instead of software memorizing a whole image it will only memorize parts of it.


Cell Phones

A hand radio owner named Nathan Cohen was having difficulty with signals. His radio could only get a few frequencies and his large satellite dish was making his landlord upset. After Cohen went to a speech given by Mandelbrot and there he learned about fractals he had a solution. He decided to make an antenna in the shape of the Koch Curve, and amazingly it worked the first time he used it. Cohen found that antennas could be smaller and more efficient when they showed fractal patterns.


Cohen discovered this around the time when cell phone companies started to offer their costumers products like Wi-Fi, Bluetooth, and Push to Talk. The problem was that each of the different services ran off of different frequencies. To solve this cell phones needed to have an antenna for each frequency, or cell phones could use fractal chips.


Cell phones now have little chips inside of them that receive calls, access Internet, and allow for Bluetooth. These chips are shaped like fractals. The chips allow phones to use each different frequency without having ten different antennas. This is because the chips show self-similarity, which allow it to work better.



 Fractal geometry can be used to explain how the stars are dispersed and how the planets behave.

Stock Market

The stock market goes up and down and changes constantly. The patterns of the stock market are hard to explain mathematically and are even harder to predict changes in. Fractal geometry can help describe it.


Before, concrete dissolved when water came through. Then at a conference on fractal applications in 2004, a speaker introduced an new type of concrete that is stronger, durable, and based off of fractals.

Sound Blocking Walls

Highway noise is a problem for people living near them. The flat walls designed to soften the noise were useless, because the noise that hit them bounced off and made things worse. Then a wall was created with a fractal surface. Now the noise is absorbed not moved.



Fractal Geometry has effected the twenty first century. It is continually applied to more subjects. It is really important form mathematics and is worth studying. In the future technology may see much advancement because of fractal geometry. There is no telling what can be done with math.







Movies like Star Wars were animated using properties of fractals.




















A chip in your cell phone that has a fractal shape allows for it to make calls.