Can you see fractals in the treetops?
A pattern that knows itself, like the laughing Buddha
Meditating under the Bodhi tree.
Branch by twig, and twig by branch,
Spinning, whirling, multiplying –
Writing into the sky.
Count the spirals on a pinecone:
Eight, thirteen, or twenty-one;
Knowingly, they turn to the centre,
while Fibonacci’s rabbits dart across footpaths,
scurrying onto their next adventure.
In the stillness of the hummingbird’s flutter,
Swirling eights form a sequence:
Down and around, up and through –
Weaving a piece of the infinite.
Numbers come to life around me,
Tallying nature’s score;
The gentle stream carries eternal sounds –
Leading us to that without limits.
* * *
This poem is inspired by my daily walks to the Beaver Pond in Kanata (my current home), where I witness the beauty of nature every day and often relate it to the beauty of mathematics. I tutor kids in math, and I’m always looking for creative ways for them to learn and appreciate math, beyond the standard curriculum. One way is to recognize that there are definite patterns in nature, which make it even more beautiful – you can literally see fractals in treetops, the golden ratio at play, and spirals in flowers and pinecones that follow the rules discovered by the mathematician Leonardo Fibonacci.
A few years ago, I was asked to do a creative writing assignment on choosing a shape for a story of my choice. I had chosen the Ramayana (an ancient Hindhu epic), and I found it impossible to choose a linear shape to represent such a mystical sequence of events. The only phenomenon I could think of was a fractal, which is a pattern that repeats itself based on a defined set of parameters. The Fibonacci sequence is as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …….
Each number in this sequence is the sum of the two numbers that preceed it. These numbers appear everywhere in nature – seashells, trees, pinecones, etc. If you count the spirals on the bottom of a pinecone, you will see that the number of spirals that weave to centre will most likely be one of the Fibonacci numbers. I commonly find pinecones that have either 8, 13, or 21 spirals. Next time you pick up a pinecone, count the spirals and see if the number is in the Fibonacci sequence!
Fibonacci also discovered rules that predict how rabbits multiply – as commonly known, rabbits are pretty frisky and tend to multiply rapidly. I am lucky to see rabbits everywhere I go in Kanata, and I especially find their fluffy white tails so adorable. Rabbits are known for eating twigs, grass, herbs and clover; four-leaf clover if they’re lucky.
Alright, I hope I’ve managed to convince you that there is more to math than trigonometry and boring equations – it may even make you appreciate the beauty of the universe a little more!