Juliet Bennett's Blog

The Koch Snowflake: Fractals

11 Feb ’11 4 Comments Written by Juliet Bennett

A fractal is a shape that you can split into parts, zoom in, and discover the same or similar shape, times infinity. It’s almost magic, this pattern which extends outward and inward, seemingly to infinity. I’ll use the Koch Snowflake among others examples of fractals to introduce what I find a very exciting concept it to you.

If this is the first you’ve heard of fractals, the best introduction is the Mandelbrot Fractal Adventure:

Let’s look at a few in nature:

Lungs [1]

Trees [2]

Ferns [3]

Cauliflower [4]

Blood vessels [5]

Lightning [6]

Closer look at lightning

And closer still

Oceanwaves [7]

The pattern of of and inside the wave:

Coastlines [8]

How does a fractal work?

Let’s look at a snowflake:

[9]

Each line is divided into three and an additional line to the same length added. This is then done to the next set of lines, and the next set, and so on to infinity. The last youtube clip in this entry gives a more detailed description of this process.

The mountain example is pretty cool too:

[10]

This guy does a great job explaining the mathematics behind it:

“Fractals demonstrate an infinite perimeter with a finite area” – now that’s an idea to ponder for a while…

References & sources:

[1] Lungs http://gaiathelivingearth.blogspot.com/2009/07/fractals-in-nature.html

[2] Trees

Fractal tree, made from using a “Lindenmayer system”.This work has been released into the public domain by its author, Solkoll.

[3] Fern http://www.rogerolivella.net/insula/en/descripcio.htm

[4] Cauliflower http://www.math.toronto.edu/~drorbn/Gallery/Plants/Cauliflower-1.html

[5] Blood vessels http://www.lionden.com/fractal_body.htm

[6] Waves http://mathpaint.blogspot.com/2008/06/fractal-waves.html

[7] Lightning – the last two also by Solkoll the first from a blog site that didn’t have copyright – if anyone knows who I should attribute it to please let me know.

[8] Coastlines http://bidhanr.wordpress.com/2010/09/13/fractals/

[9] Fractal Snowflake Graphic by António Miguel de Campos (self made based in own JAVA animation) [Public domain], via Wikimedia Commons.

[10] Fractal Mountain Graphic by António Miguel de Campos (self made based in own JAVA animation) [Public domain], via Wikimedia Commons.

Also good reference is: Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company.

Truth
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4 Comments

  1. Vale
    11 Jul ’11    

    Hi Juliet,
    great website. the first photo looks like you are having your head pierced! kind regards,
    Vale

    Reply
    • Juliet Bennett
      19 Jun ’12    

      I just saw this Vale! Thanks for the comment 🙂

  2. Me
    18 Jun ’12    

    “Koch Snowflake”, not kock

    Reply

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