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Fractals

High School

Definition

Fractals are geometric shapes where parts resemble the whole (self-similarity). They can have non-integer dimensions.

D = (log N)/(log s)

Fractal dimension (N: pieces, s: scale)

z_n+1 = zₙ² + c

Mandelbrot set iteration

Example 1

Find the dimension of Sierpinski triangle.

Example 2

What is the dimension of Koch snowflake?

Discovered by: Benoit Mandelbrot (1975)

Mandelbrot coined the term 'fractal' and systematized the field.

Natural terrain generation

Blood vessels, lung structure

Fractal antennas