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I have long been fascinated by number sequences and finding the patterns within them.  This brings me to a fun topic . . . Fractals!

What are Fractals? – According to the Fractal Foundation, a fractal is a never-ending pattern that repeats itself at different scales.  This property is call “Self-Similarity”. This means that as you look closer and closer into the details of a fractal, you can see a replica of the whole.  What you may not know is that fractals of been of interest to people for over 2,000 years when Euclid, a Greek mathematician, claimed a straight line segment can be prolonged indefinitely . . . although, Mandelbrot stated the new fractal geometry is different . . . Oh, those crazy mathematicians!  (But, now I’m starting to sound like an episode of The Big Bang Theory . . . so, so I’ll move on)

Frankly, I think it’s easier to understand fractals by seeing an example.

Step 1 – Take Triangle

Triangle - step 1

Step 2 – Subdivide by three

Triangle - step 2

Step 3 – Subdivide again by three

Triangle - step 3

Step 4 and beyond  – Keep subdividing by three

Triangle - step 4  Triangle - step 5  Triangle - step 6

This can literally go on and on

Let’s see with a simple line

Fractal line

We can do this with a number of elements

Fractal graphic

Okay, so this is possible in graphics, but you may be wondering . . .

Are there naturally occurring fractals? – You may not know it, but we’re surrounded by fractals every day.  From the veins in a leaf, to the branches on a tree, the structure of a snowflake, mountain ranges, rivers, lightning bolts, and much more.  We can’t go a day without fractals.  Below are a few examples of naturally occurring fractals.

Fractal snowflake Leaf fractal #2 Leaf fractal Lightning fractal

Graphical fractals

Fractal #1 Fractal #2

As a design approach, fractals can be very inspirational and there are some easy on-line resources for generating your own fractals

Illuminations – http://illuminations.nctm.org/ActivityDetail.aspx?ID=17

Illuminations

Easy Fractal Generator – http://www.easyfractalgenerator.com/

Easy Fractal Generator

Just looking at fractals can be inspirational and there are on-line galleries and other resources available for viewing

Fantastic Fractals – http://www.fantastic-fractals.com/index.html

Fantastic Fractals

Fractal Foundationhttp://fractalfoundation.org/

Fractal Foundation

Even googling the word “fractal” will generate many examples.  Enjoy exploring fractals and discover ways to use them as inspiration.

Update . . .

Here are a couple of simple fractal-like drafts . . . a sis-shaft Bronson lace and a 16-shaft summer & winter

6-shaft Bronson.dtx

 

16-shaft fractal draft as summer & winter.dtx

 

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Comments on: "These are a few of my favorite things: #29 – Fractals" (14)

  1. I highly recommend Electric Sheep – http://www.electricsheep.org/ – it’s a really beautiful fractal screen-saver, and it downloads new “flames” when it’s in idle mode!

  2. Nancy C. said:

    For further investigation, here’s a link to an excelllent PBS program on fractals – Fractals – hunting the hidden dimension. http://www.youtube.com/watch?v=LemPnZn54Kw
    About 25 minutes in is an interview with a clothing designer and her use of fractals.

  3. That was a fun blog entry, Robyn, thanks!

  4. Diana D. said:

    I have always enjoyed fractals and think they are fascinating. However, I am completely stymied when it comes to using them as inspiration for my weaving. Do you have any personal examples of weaving that was inspired by fractals?

    • loomchick said:

      I’ve added a couple of simple examples of fractals as weaving drafts . . . a six-shaft Bronson lace and a 16-shaft summer & winter. I hope this helps.

      • Diana D. said:

        Thanks, the drafts do give me some ideas.

      • loomchick said:

        Terrific! I’m sure others have better examples of fractals in weaving . . . Perhaps it would be fun to have a fractal draft exchange some day.

  5. BarbaraP said:

    I have done what they are now calling “Wiggle Crochet” for years, copying my grandmothers pot holder from the 1940’s, and I considered trying to cover each side of a square of filet crochet with the double crochet ruffle without having to cross over or break the yarn as a kind of fractal exercise. There is a mathematical group on Ravelry that do a lot of fractal and mathematical based knit and crochet. Did you know you can crochet a Sierpinski triangle? Cool to work out something in weaving too! Yeah I am a nerd and I love Big Bang Theory.

  6. Phil Blake said:

    Hi Robyn, these photos are amazing!

    I am currently writing my masters dissertation about flows through fractals and was wondering if I could use some of your images in my thesis?

    • loomchick said:

      Thank you, Phil. I’m glad you liked my blog post on fractals. For your thesis, it would be okay to use some of the images.

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