Fractal Geometry

In the relatively short time since its discovery, fractal geometry has informed breakthroughs in numerous areas of science and industry—from biology, to telecommunications, to computer graphics. The depth and breadth of these applications suggest that we have only just begun to scratch the surface of what fractal geometry can teach us.

Fractals in cinema and graphic design

After Loren Carpenter, co-founder of Pixar Animation Studios, read Benoit Mandelbrot’s Fractals: Form, Chance, and Dimension, he began experimenting with fractals to make his computer graphics look more realistic. This technique gave rise to software programs now widely used across the computer graphics industry to create special effects, including fictitious landscapes and imaginary worlds—such as the Genesis planet sequence in Star Trek II: The Wrath of Khan and the damaged Death Star in Return of the Jedi.

Fractal image compression

Fractal compression converts images consisting of random information into fractal code—saving only a small, representative amount of information that is later used to re-create the original image. Since the fractal image is now code instead of pixels, file size is drastically reduced and the image can be scaled to any size without losing its sharpness.

Fractals in biology

Fractal geometry is being used in the biological sciences to accurately model the human lung, heartbeats and blood vessels, neurological systems and countless other physiological processes. Doctors and researchers are now using the mathematics behind fractal geometry to build models that they hope will identify microscopic patterns of diseases and abnormalities earlier than ever before.

Fractals in the stock market

In light of the financial crisis that began in 2007, many market theorists are turning to the teachings of Benoit Mandelbrot, whose fractal approach to price variation revealed that a crash was not as improbable as forecast by conventional wisdom. Mandelbrot dismissed the theory of efficient markets as simplistic and overly generalized, commenting that the world is not tidy or infinitely stable—turbulence is a natural unavoidable force. These views are discussed further in Mandelbrot’s 2004 book The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward, co-written by Richard L. Hudson.

Fractals in climate science

Scientists have recently shown that the distribution of large branches to smaller branches in a single tree exactly replicates the distribution of large trees to smaller trees in an entire forest. Research is currently underway to use this information to measure how much carbon dioxide a single forest is capable of processing. From there, scientists will be able to apply their findings to every forest on earth, quantifying how much carbon dioxide the entire world can safely absorb.