Fractals Jennifer Trinh

Fractals

• Jennifer Trinh

They’re SO BADASS!

Basic Idea

With Euclidean geometry…

Exact Self-Similarity: Koch Snowflake

Approximate Self-Similarity: Mandelbrot Set

Statistical Self-Similarity

Hausdorff-Besicovitch Dimension: Fractal Dimension?

• relationship between the measured length and the ruler length is not linear, i.e.: 1 dimensional

• The fractal/Hausdorff-Besicovitch dimension is d in the equation N = M^d, where N is the number of pieces left after an object is divided M times.  E.g., we divide the sides of a square into thirds, we have 9 total pieces left.  9 = 3^2, so the fractal dimension is 2.

• More formally seen as log(N(l)) = log(c) - D log(l)

• Doesn’t have to be an integer

Generating Fractals

“Measuring” Fractals

Sources

• http://tiger.towson.edu/~gstiff1/fractalpage.htm

• http://www.fractal-animation.net/ufvp.html

• http://local.wasp.uwa.edu.au/~pbourke/fractals/

• http://www.fractalus.com/info/layman.htm

• http://en.wikipedia.org/wiki/Fractal

• http://mathworld.wolfram.com/KochSnowflake.html