Adventures with Ideas: Truth, Beauty and the Paradoxes of Life
Juliet Bennett's Blog
  • About
  • My Story
  • Research
  • Photography
  • Modeling
  • 2009
  • 2010
  • 2011
  • 2012
  • 2013
  • 2014
  • 2015
  • About
  • My Story
  • Research
  • Photography
  • Modeling
  • 2009
  • 2010
  • 2011
  • 2012
  • 2013
  • 2014
  • 2015
  • Home
  • Truth
  • The Koch Snowflake: Fractals

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
Fractal, philosophy
Similar posts
  • Business leadership in climate change — I am consistently surprised by the initiative and leadership taken by businesses to address the climate crisis. Not all businesses obviously (e.g. ExxonMobil, the Koch brothers and the other vested interest that have funded climate denial movement and created vast climate confusion), but MANY businesses and business analysts, scholars and consultants are doing a extraordinarily better job than many governments [...]
  • Orwellian Australia: the “[Un]F... — On 15 April 2016 the so-called “Fairer Parental Leave Bill 2015″ was “Lapsed at prorogation” and the current status on the bill is (thankfully, at this stage) “Not proceeding”. I’m not sure whether this is a permanent status, or whether they just ran out of time and will return to the bill later…  When I see the word “fairer” associated with this bill [...]
  • A new lens to view the world: the wor... — My PhD is essentially an exercise in communicating and examining the potential for an  alternative worldview to the mechanistic materialism offered by process philosophy to contribute to addressing structural forms of violence and working toward peace. Process philosophy is too rarely taught in university philosophy as the current fashion there is divided between analytical or postmodern navel gazing. Yet process [...]
  • Thoughts on a morning walk — On my walk this morning: –       I realised that truth, reality, and illusion, are completely relative and self created –       the truth of a religion is truth for that person, it is made real by the stories that are told, and because each moment is in a way timeless, these truths are eternally real –       yet when truths are examined [...]
  • Boundaries between Self and World — “Your skin doesn’t separate you from the world; it’s a bridge through which the external world flows into you, and you flow into it.” More Alan Watts? Yes, it’s always a good time for more Alan Watts. Over and over and over, repeat. “The whole world is moving through you, all the cosmic rays, all the food you’re eating, the [...]
Parkinson’s Law: Using Time to Your Advantage
Is “God” a Fractal?

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
    • Juliet Bennett
      19 Jun ’12    

      Haha I know. It was a joke lol

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

TRUTH

BEAUTY

ADVENTURE

ART

PEACE

  • Popular
  • Recent
  • Comments
  • Is “God” a Fractal?
    15 Feb ’11
  • Is Lindt chocolate slave chocolate?
    11 Sep ’09
  • Creativism – a philosophy for life
    10 Sep ’09
  • Free Documentaries: The Truth Is Free
    17 Apr ’10
  • Coming to grips with the elephant in the room
    28 Jun ’10
  • Optimum Trajectory, swimming against the current, and man who stare at goats.
    4 Aug ’10
  • A short biography
    2 Sep ’09
  • Sex or chess? Peace, the world’s trump card
    13 Apr ’10
  • Alan Watts Fan Club
    3 Dec ’12
  • The Very Short Life and Times of Me and Kombi Xee
    23 Feb ’11
  • My policy wishlist for Australia’s response to climate change
    17 Jan ’20
  • Business leadership in climate change
    1 May ’19
  • A story of (mis)fortune: the farmer and his son
    8 Oct ’18
  • What is life really about?
    1 Mar ’17
  • Why the right (brain) is right…
    22 Feb ’17
  • New life: reflections on being a new mum
    29 Dec ’16
  • Orwellian Australia: the “[Un]Fairer Parental Leave Bill 2015”
    1 May ’16
  • Alan Watts’ ‘dramatic model’ and the pursuit of peace
    18 Mar ’16
  • A new lens to view the world: the world as process
    14 Jan ’16
  • 2015 in review
    1 Jan ’16

Adventures with Ideas... on Facebook

Archives

Categories

  • Academic (35)
  • Adventure (119)
  • Beauty (23)
  • Featured Posts (10)
  • Peace (124)
  • Random Life Stuff (102)
  • Truth (164)
Constitutional Recognition

Rights of Indigenous Peoples: A Personal Statement

As a "non-indigenous" Australian living on what was once the land of the Cadigal and Wangal Wangal communities, I wish to acknowledge the inter-generational responsibility that I feel toward the colonial past. As a beneficiary of "White Australia", to the Eora people of Sydney, I request your forgiveness. I stand in solidarity with your rightful demands to self determination and active participation in governmental decisions, and I hope I may learn from your eco-spiritual connection. May we, as Tom Trevorrow of the Ngarrindjeri puts it, learn to 'respect, care and share' the gifts that our planet offers us.

Tags

Alan Watts Atheism Big History Bridge Series Central America Chocolate climate change Conflict Transformation Creativism Ecology Europe God Health India India/Nepal inspiration Life in Oz Life philosophy Meaning of life Modeling My Brazilian My Christian Journey Narrative Narratology Occupy optimal trajectory Panentheism peace philosophy Photography Politics population Potentialism poverty religion slavery social construction South America The Pyramid Travel United States War What is God Wikileaks Yoga

Related posts

  • Fractal
    • Is “God” a Fractal?
    • Microcosms and macrocosms – we are specks of dust in a giant’s eye
  • philosophy
    • Optimum Trajectory, swimming against the current, and man who stare at goats.
    • Joseph Campbell – The Hero’s Journey
    • Disasters and Delhi
    • Curing my incurable optimism
    • Modeling Tips: Where to Begin

Donation

evolve theme by Theme4Press  •  Powered by WordPress