Last week, child number three and I spent time watching Vi Hart videos on the Khan Academy website. The films lure you in with the hypnotic into “so you’re math class and your teacher is droning on about –insert math principle- and you’re bored so you start doodling”. She then fills her notepad with doodles that cunningly illustrate the math principle that the fictitious teacher was unable to engage you in. As a consequence we have been trying to make hexaflexagons, drawing snakes that slither under and over their own bodies and replicating Sierpinski’s Triangles. The fast pace of Vi’s speech, the many coloured sharpies and the casual reference to mathematicians as though they are friends has a hypnotic effect, Vi is an effectively eccentric tutor. Number three isbusily filling her notebook with colours and shapes which are the basic tenets of patterns.
I find that drawing patterns has a meditative effect. I start with a blank piece of paper, then I invent a rules about colour, line or shape and proceed to fill the page using the rule. I then assess the result and puzzle over the next idea. I realise that I use a pattern to make a pattern.
This making of patterns often leads me in to a state of flow, which Csíkszentmihályi describes as “an intrinsically rewarding or optimal state that results from intense engagement with daily activities". Conversely, I often start to make patterns to disengage from the intense engagement of the demands of my progeny. I also find that getting into the flow can solve problems seemingly unrelated to the task at hand. Nice huh?!
The Sierpinski Triangle is a fractal construction: the image is self-similar and therefore similar at any point, by magnification or reduction, regardless of scale.