FRACTAL CROCHET?? What’s Cauliflower Got To Do With It?

What does cauliflower have to do with crochet?  Not much.  This is just an example of an everyday fractal.  Fractals are amazing mathematical shapes first described by Gaston Julia and Benoit Mandelbrot.  You can google those guys and read til the end of the internet – and if I did that, I still wouldn’t understand the math.  But, I do know what I like when I see it.  This stuff is truly amazing.  So, go do some research.  I’ll wait……

Above is a 3-D fractal ‘cube’.  Does it remind you of anything?

This image of a Herrschner’s Tumbling Blocks afghan could certainly be adapted to more closely resemble the Fractal image above.

The Sierpinski Sieve is the simplest (not to crochet but to visualize) crocheted fractal.  Here’s a schematic:

Not too hard to figure out how we can use this fractal in crochet.  My friend Ronnie crocheted a lovely (if tedious to complete) Sierpinski Sieve Shawl using two strands of a thread about size 10.  It is a dazzling work of art.  Not that you’ll see me making one anytime soon!

I am no mathematician.  Math was always my worst subject in school.  But, I have an instinctive appreciation of the pristine nature of numbers.  The numbers that I can comprehend, and the theories regarding them, are black and white.  The answer to a problem is either right or wrong.  There is something elegant about that.

So, starting with the humble image of a slice of cauliflower, we see how the smallest component of a thing is the same shape as the thing overall.  Look at the veins of a leaf on a tree and you’ll see the shape of the entire tree.  How cool is that??  Same works for coastlines around the world, for snowflakes, for bacteria, for lots of stuff.  That’s fractals.  Show me how we can apply this to crochet.  Please!