MelissaA
Brenton
Shilpa Karhik
A bluffer's guide to chaos theory 3
July 24th 2006 06:01
Today's post is going to be about fractals, which are an important aspect of chaos theory.
A fractal is technically defined as an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension, but a common definition is a shape that appears similar at large levels of magnification.
Benoit Mandelbrot was one of the first people to present these in the form they are currently studied and he coined the term fractal. Many of his ideas were developed in the study of coastlines, which are themselves fractal.
Fractals are defined by their level of self similarity, which ranges from exact self-similarity, where the fractal is identical when viewed at different magnifications, and statistical self similarity, where the fractal has some statistical features that are present at different magnifications.
Fractals can be found in nature, famously in the forms of snowflakes and fern trees and they have been discovered in a variety of different areas.
My next post will be on the history of chaos theory.
Adam
A fractal is technically defined as an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension, but a common definition is a shape that appears similar at large levels of magnification.
Benoit Mandelbrot was one of the first people to present these in the form they are currently studied and he coined the term fractal. Many of his ideas were developed in the study of coastlines, which are themselves fractal.
Fractals are defined by their level of self similarity, which ranges from exact self-similarity, where the fractal is identical when viewed at different magnifications, and statistical self similarity, where the fractal has some statistical features that are present at different magnifications.
Fractals can be found in nature, famously in the forms of snowflakes and fern trees and they have been discovered in a variety of different areas.
My next post will be on the history of chaos theory.
Adam
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