Binary Bonsai and Other Mathematical “Plants”

A "Binary Bonsai" tree. Copyright Madeleine Shepherd. Used with permission.

A “binary bonsai” created using an algorithmic knitting process. Image copyright Madeleine Shepherd. Used with permission.

Many of us have seen Fibonacci numbers in sunflowers and hyperbolic curvature in kale leaves. Botanica Mathematica, “a textile taxonomy of mathematical plant forms,” takes mathematical-botanical correspondences like these and throws in a little fiber art. “The Botanica Mathematica project is about using simple mathematical rules to generate pieces of knitting or crochet,” says one post. The blog is a companion to an art exhibit in progress. Later this year, Botanica Mathematica creators Julia Collins and Madeleine Shepherd will put together an art installation of the pieces they make and receive from knitters and crocheters around the world. Shepherd says that pieces have been donated from England, Scotland, Germany, the Netherlands, and the US, and anyone is welcome to contribute.

Collins and Shepherd were inspired to by two 2013 theme years: Mathematics of Planet Earth, which I wrote about in April, and the Year of Natural Scotland. Collins is a Ph.D. mathematician who works as the mathematics engagement officer at the University of Edinburgh (what an awesome job!), and Shepherd is the communications officer at the International Centre for Mathematical Sciences and a textile artist at Plum&Pepper Studio. Collins and Shepherd have previously collaborated on other science communications projects including The Mathematician’s Shirts, in which they created mathematical sculptures from, you guessed it, shirts. I’m sorry that I wasn’t aware of that project when it was going on, but I’ll be mining it for ideas for my own sewing.

The Botanica Mathematica blog has instructions for making mathematically inspired “plants” such as binary bonsai and knitted chanterelles. If you’re a knitter, crocheter, or otherwise crafty with textiles, you can contribute to the art installation by sending your mathematical textile “plants” to the address in this post. The project reminds me of the beautiful crocheted “coral reefs” I’ve seen based on Daina Taimina’s awesome hyperbolic crochet.

I’ve really enjoyed the posts on L-system knitting. An L-system, or Lindenmayer system, is a way to generate a new output based on previous inputs. They are algorithmic, so they feel very familiar to mathematicians, but if I understand correctly, Lindenmayer was a plant biologist who originally developed L-systems to study the growth patterns of algae. The pattern in the post called “Chaotic knitting” reminded me of George Hart’s video “Shell Games” for Simons Science News. It’s cool to see large triangles grow out of what looks like chaos at the beginning.

As a mathematician, sewist, and beginning crocheter, I love the crossover appeal of Botanica Mathematica and the way Collins and Shepherd are using it to trade ideas with people who might not normally think about math very much. They participated in Edinburgh’s Maker Faire earlier this year, and they started a Botanica Mathematica group (login required) on the knitting/crochet site Ravelry. “There have been some great discussions on the message boards there, with people taking our ideas in new and unexpected directions,” Collins wrote in an email. “For example, after reading the pattern for the Binary Bonsai, one user thought about using binary numbers to write secret messages into a knitting pattern. They then converted a stanza of Robert Burns’ ‘Tam O’Shanter’ into binary code and used it to knit a lace scarf!”

I hope Collins and Shepherd keep updating the blog with more instructions and pictures of finished projects, and I’d love to see some plant biologists chime in with their ideas as well. In the meantime, I might need to pull out my crochet hooks and make some L-systems!

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