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
Step 2 – Subdivide by three
Step 3 – Subdivide again by three
Step 4 and beyond – Keep subdividing by three
This can literally go on and on
Let’s see with a simple line
We can do this with a number of elements
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.
Graphical fractals
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
Easy Fractal Generator – http://www.easyfractalgenerator.com/
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
Fractal Foundation –http://fractalfoundation.org/
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
Comments on: "These are a few of my favorite things: #29 – Fractals" (14)
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!
Looks like a keeper. Thanks for sharing!
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.
Thanks for sharing, Nancy! Looks like something I need to check out.
That was a fun blog entry, Robyn, thanks!
Thanks! I’m glad you liked it.
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?
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.
Thanks, the drafts do give me some ideas.
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.
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.
Very cool! Always nice to find another fractal fan!
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?
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.