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Transcript of Fractal Geometry
What is Fractal Geometry?
Michael Schmidt, Jayson Boucher, and Kelsey Charnawskas
Nature is rough and, for many years, was impossible to measure.
Mandelbrot - if you can identify an essential structure in nature, the concepts of fractal geometry can be applied in order to understand the parts. A hypothesis can then be made about what the structure will become in the future.
Most basic example: a tree
Von Koch Curve
Mendelbrot Set: Z_0=0 and C=a+bi
Human heart beat
Dispersion of blood
Detection of cancerous cell formations
Cancer cells viewed using Reflection Interference Contrast Microscopy Images
First considered in the 17th century by mathematician and philosopher Leibniz who measured recursive self-similarity in the sense of a straight line.
1975 - Benoit Mandelbrot coins the term after working with computer-constructed visualizations.
Derived from Latin word
meaning "broken" or "fractured"
"A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole"
Features include a fine structure at arbitrarily small scales, a simple and recursive definition, and are too irregular to be easily described using traditional Euclidean geometric language.
Most important, they are
or figures made up of other figures that are similar in shape.