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That fractal that's been up on my wall for years
Content Warning: Math, Handwaving I spent a lot of time doodling in middle school in lieu of whatever it is middle schoolers are supposed to be doing. Somewhere between the Cool S’s and Penrose triangles I stumbled upon a neat way to fill up graph paper by repeatedly combining and copying squares. I suspected there was more to the doodle but wasn’t quite sure how to analyze it. Deciding to delegate to a future version of me that knows more math, I put it up on the wall behind my desk where it has followed me from high school to college to the present day.
If you have graph paper and free time you can try out the steps for yourself – it’s fun to translate and trace the contour of the previous state and watch things lock into place like a puzzle. It turns out my younger self left behind the perfect gift in the form of a scavenger hunt across the domains of fractals, number systems, linear algebra and higher dimensions. Hopefully by writing and visualizing my lines of reasoning I’m able to make the connections a bit more accessible for future fractal fiddlers finding themselves falling face first down the same rabbit hole.
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