Romanesco Fractal

The first time my daughter asked, "Mama, what does “infinity” mean?" I stumbled over a technical answer and botched an opportunity for something magical like, "It is how much I love you."  Today, an opportunity to revisit the subject arose as organically as the box in which it came.

We support Riverdog Farm, a certified organic CSA and Thursdays are our veggie box day.  Eating seasonally is an integral part of our curriculum and opening the box on veggie day feels like Christmas morning to my whole family.  We’re always surprised and delighted by the wonders inside.  What’s more, eating seasonally and locally helps us feel our connection to the earth and her rhythms.  As a homeschooling parent and a mother endeavoring to teach her child environmental responsibility, I’ve come to honor and rely on this rhythm.

While picking up our veggie box today, I felt especially grateful for the opportunity to belong to a CSA and reflected on the values this is instilling in my little one.  We talked about how the produce at the grocery store comes long distances on trucks that use stinky fossil fuels and how that affects the environment, we talked about the importance of supporting our community, and how food tastes better when it’s fresh from the farm.

By the time we got home, I felt satisfied with the organic lesson about supporting our CSA.  This was just the beginning of today’s homeschooling highlights.  We opened our box and discovered a fractal vegetable, Romanesco Broccoli (Brassica oleracea).  The bright green flower is composed of spirally arranged segments that are identical copies of the whole flower.  The copying process continues ad infinitum as a three-dimensional fractal form.  The mathematical beauty and simplicity of this flower never ceases to amaze me.  School was now officially in session.

Discussing infinity with a Kindergartner might seem daunting but it becomes magical when demonstrated on the dinner table.  Since botching my first attempt at explaining infinity last year, I’ve gotten a little better at seeing through my child's eyes.  Last summer, we even had some fun growing Fibonacci Sunflowers in our Edible Classroom.  While grasping an abstract idea may be a stretch for most kids, understanding something they can see, touch, taste, smell and feel usually works.  Today, we literally held infinity in the palm of our hand.  This is nature-based learning.

Looking at the Romanesco, we can see that it’s cone-shaped.  Each of its cones is a replica of the whole flower.  Each bud is composed of a series of smaller buds; all arranged in yet another logarithmic spiral.  I hear Jefferson Airplane singing, White Rabbit.  “Go ask Alice, when she’s ten feet tall.”  It’s a pretty psychedelic vegetable!

After eating all of our math, we popped open the laptop and looked at a few other images of fractals.  Two more from nature are the fern and snowflake pictured below.  All of nature is alive with language, math, and music.  We just need to slow down and look more closely.

Later, we'll draw some of our own fractals -- a big shape with of each of its parts as identical copies of the whole.  Maybe I’ll dig up some literature on the universe as fractal and work on a Parallel Worlds Thematic Unit.  We've read (and seen!) so many archetypal stories with the “magical worlds” premise (Chronicles of Narnia, Wizard of Oz, and Golden Compass) that stepping through magical gates into other worlds has become part of my daughter’s regular imaginative play.  Eventually we will discuss the many-worlds interpretation of quantum physics but we’ll have to schedule a field trip to the Exploratorium for that one.  For now, just keeping her mind wide open and pointing her towards math and science is enough.

It takes an open mind to see the magic in the world.  We can't be so full of ideas that we're not open to the infinite possibilities before us.  This is the magic of childhood.  Nurturing that creativity is exactly what I hope to do when I introduce concepts like fractals to my five year old.  One of my most important jobs as her teacher is to pique her curiosity in all subjects.  If I can do that and get her to eat her vegetables at the same time, I think we both get an A+ for the day.