Self-similarity: childhood sketch to field of study
When I was a little girl, I used to draw sketches of zig-zags on big sheets of paper. I used to see how many patterns I could create that were self-similar; the initial zig-zags would form part of a larger zig-zag, which would form part of an even larger one, etcetera. I never really knew that there was anything significant about this, but many, many years later, I met somebody who was obsessed with fractals.
Google Images 2008
Fractals are beautiful self-similar patterns which are connected to Chaos and Complexity Theory. I didn’t know much about them at the time, but listened with interest to his perceptions of them and their relevance to the planet and our daily lives. A few years later again, I did a subject called ‘Environment and Health’ at university, which included a large section on Chaos theory, its links with planetary health, human health and man-made systems such as the hierarchical, self-similar structure of businesses.
I learnt that coast-lines, broccoli and the human small-intestine (villi and micro villi) are all self-similar and that the less information-rich a system is, the more vulnerable it is to significant perterbations (such as an orchard of apples whch may be wiped out by a single pathogen compared with a rainforest climax community with an exponentially larger gene pool). I was reading Seymour Papert’s article entitled: ‘The Gears of My Childhood’ which communicates his spatial understanding of gears and cogs from an early age which led to his love of mathematics years later. I’m no mathematitian or Steven Hawking, however it’s interesting to see how children’s interests can be directly linked to their cognitive development and later achievement.
We should take note of this in the classroom and make sure to nurture our children’s hobbies, talents and imaginings, as we never know where they could lead!
