binary space partitioning the world
Last tended to on October 13, 2024
the world is divided into 4 quadrants: 00, 01, 10, and 11 (starting with the top left, then top right, then bottom left, then bottom right.) each of those is divided into 4 quadrants, and so on. we can represent any location on earth as a string of 0’s and 1’s, where each 2 bits represents a quadrant.
for example, my childhood home is at 0011000000111011000000 (last few bits left off for privacy…)
mt everest is around 011001111101000101
i encourage you to go down the rabbit-hole to your home, workplace, or a favorite spot in the world. then, once you get to the bottom, zoom back out to see the fractal you’ve created.
have at it~ inspired by the CGP Grey A4 paper video
metanote; while i was writing this note, copilot gave me the following suggestion:
Which…not only is a valid youtube video, but it’s a 3blue1brown video on the very topic of fractals. Before I’d even written the word fractal, or self-similar, or anything in this document. Kinda crazy, right?
fun observations / thoughts
- the world is in the order of magnitude 234 larger than my house.
- you can really see how messed up the Mercator is by the shapes of the quadrants in the far north
- many different ways we could do this– just have to map a different fractal onto a different projection. e.g. we could do Sierpinski fractals on top of Buckminster Fuller’s Dymaxion map, or hexagons, because, you know, they’re the bestagons (@cgpgrey).
- If you live in two different places, what’s your Last Common Ancestor in the binary tree?
Links to “binary space partitioning the world”
obsessed with geography..maps..? what do you call it (obsessed with geography..maps..? what do you call it)
for that reason, i love trawling wikipedia pages about the extremes of the earth, zooming in on random spots on google earth, watching cgp grey videos on the matter, and creating lil experiments such as one locating yourself anywhere in the world with a binary number.
i made an experiment which allows you to recursively divide up the world into binary spaces and locate yourself.