I love crochet as an artist and creator, but I also love the way it can so easily relate to math!
I wrote previously about hyperbolic crochet and how this mathematical concept can be modeled in crochet because of the way crochet stitches can be increased in every row.
There is another concept that exists in math and nature that can be modeled in crochet, and that is fractals.
If you’ve never heard of fractals before, you may be surprised to learn that they’re all around – you’ve probably seen some in nature today, and they even exist within your body!
But what is a fractal, and how can they be represented in nature, mathematics, and crochet?
What Is a Fractal?
In the simplest terms, a fractal is a never-ending pattern. Fractals have a property called “self-similarity,” which means that they look approximately the same on any scale.
No matter how “zoomed in” or “zoomed out” you are on a fractal, it looks basically the same.
We see examples of fractals in nature, in mathematics, and even in art!
Fractals in Nature
An oak tree is an example of a branching fractal in nature. It is formed when the seed sprouts and then branches again, and again, and again.
You can see the same branching pattern when you look at a small part of the tree that you see when you look at the entire tree.
Our lungs are branching fractals as well, with patterns that are very similar to a tree’s branches.
Nature also contains many spiral fractals. Hurricanes are one example. There are also many living spirals in nature, such as the agave cactus, which grows new pieces at a fixed angle, forming a spiral.
Pinecones and sunflowers build their fractal patterns in the same way.
Fractals in Mathematics
Geometric fractals can be formed by repeating the same shape and pattern at different sizes.
Algebraic fractals are created by calculating the same simple equation over and over, and always feeding the answer back into the start of the equation. The Mandelbrot Equation is a famous fractal equation.
Fractals are useful in many fields, including computer science and cancer research. For more information, check out the video below.
Fractals in Art
Fractal geometry can be incredibly beautiful, which is why one of our favorite ways that fractals are used is in art – and, of course, especially in crochet!
Spiral Fractal Crochet Table Runner
This spiral doily or table runner is a fun and visually interesting way to display fractal crochet art in your home. It’s made up of a spiral that grows as it rotates.
If you’d like to try your hand at making this fractal table runner, check out the pattern here or watch the YouTube tutorial below.
This crocheted shawl makes use of a fractal pattern, which is good news for beginning crocheters.
Since a geometric fractal is just a repetition of the same shape and pattern, this pattern only requires a few different stitches, over and over!
If you’re new to the craft and want to practice your single, double, and triple crochet stitches, you can get this pattern here.
You can practice while creating this beautiful wearable piece of fractal art!
Rainbow Fractal Table Runner
Here is another table runner that makes use of a spiral fractal pattern.
This one is done in rainbow colors, which makes it so bright and beautiful. I love the way that the spiral goes in two directions on this one, also.
Fractal Crochet Cloud Display
This art installation by Aregentinian artist and architect Ciro Najle is intended to imitate the fractal structure of clouds.
It’s called “Cumulus,” and while it’s beautiful to look at and currently displayed as artwork, it was actually inspired by a practical application.
The artist was working on a project to improve access to clean water in arid regions.
The original project used fog nets to capture moisture from the air, and this inspired Najle to reinterpret the clouds in a crochet art form.
If you’re ready to hop on a plane to visit, you can walk beneath these woolen clouds at Le Laboratoire, an art and design space in Paris that features projects combining art with science, often with humanitarian goals.
Although fractals are “infinitely complex,” the concept is really very familiar- we see fractals every day in the sky, in plants, and even in our bodies.
What do you think – will you give a crochet fractal a try?