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What is a fractal?

Contents

  • What is a fractal?
    • Examples
    • Fractals in Nature
    • Mandelbrot set
    • See also
[...] Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". [...] The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.

Source: Fractal, Wikipedia

Examples

The Rensselaer Polytechnic Institute made an applet which allows you to create fractals by yourself. So I've tried this one as a starter:

Martin Fractal #1
Martin Fractal #1
Martin Fractal #2
Martin Fractal #2
Martin Fractal #3
Martin Fractal #3

You might know this one:

Snowflake fractal #1
Snowflake fractal #1
Snowflake fractal #2
Snowflake fractal #2
Snowflake fractal #3
Snowflake fractal #3
Snowflake fractal #4
Snowflake fractal #4

Fractals in Nature

Fractals seem to appear quite often in nature. I have just re-created one that I have seen recently:

Leaf fractal #1
Leaf fractal #1
Leaf fractal #2
Leaf fractal #2
Leaf fractal #3
Leaf fractal #3
Leaf fractal #4
Leaf fractal #4
Leaf fractal #5
Leaf fractal #5
Leaf fractal #6
Leaf fractal #6
Leaf fractal #9
Leaf fractal #9

Mandelbrot set

The Mandelbrot set is maybe the best known fractal, although it is not a fractal in my opinion. It does never repeat itself.

See also

  • Fractal
  • Mandelbrot set
  • Visualization of a fractal
  • TED Talk: Ron Eglash on African fractals

Published

Jul 7, 2012
by Martin Thoma

Category

Cyberculture

Tags

  • fractal 1
  • mathematics 59

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