Searching for understanding of fractal geometry and it's hidden dimensions expressed throughout nature and the universe,
this NOVA documentary explores fractals and how they may be used to better understand the world around us, including coastlines,
rainforests, weather systems and human physiology.
Topics of this video include:
a) one of the first applications of fractal geometry when a Boeing computer scientist in 1978
applied principles of fractal geometry to create a mountain background for a plane for publicity photos.
b) Benoît Mandelbrot's forms in nature can be described mathematically," a word he
invented to describe shapes that look jagged, or broken, or that do not conform to traditional geometry.
c) fractal production, taking smooth shapes and dividing repeatedly thru iteration.
d) characteristic self-similarity, a state in which an object looks the same regardless of the distance
from which it is viewed, or in which an object's parts look similar to the whole object.
e) prior to Mandelbrot's discovery of fractal geometry in the 1970s, mathematicians had no mechanism for
characterizing erratic patterns in nature.
f) Mandelbrot noticed patterns in phone-line transmissions that reminded him of a hundred-year-old
mystery known as mathematical "monsters."
g) illustrates "monsters", the Cantor set, Koch's snowflake, and the
h) how Mandelbrot used the Julia set to create the Mandelbrot set.
i) many pure mathematicians were against Mandelbrot initially, and still today some mathematicians maintain
his work has done little to advance math theory.
j) many many examples of fractal modeling applied to everyday life, measuring coastlines,
creating special effects in film, fractal antenna efficiency, human physiology, why large animals use energy
more efficiently than small ones.
k) researchers of the Costa Rican rainforest, apply fractal mathematical modeling to determine whether
the data from a single tree can reveal information about how much carbon dioxide
the entire rainforest can absorb.