Thanks Cliff, it means a ton coming from you! The videos from you and all the other folks on Numberphile always inspired me to see the beauty in math growing up :)
I'm by no means a parenting expert, but my answer would be anything related to something they feel passion or wonder for in the moment. I snuck in a paragraph near the end about burnout. At the root of the problem for me was that I lost the feeling of fascination and curiosity I had for math and programming, and doing this write-up helped me tap into that feeling of childlike wonder that used to come easily.
Holy cow, I was expecting a quick read. Wound up having to skim some, as I need to get some work today. Will be coming back to this to play with some. Really well done!
[edit] Just noticed the article has two different numbering systems, one where 10, 20, 30, 40 are clockwise and one where they are anticlockwise. In both, 1, 2, 3, 4 are clockwise. My addition is on the second, where 10s are anticlockwise (this is what is used in the addition table).
It still works in the alternative system (14+21 should equal 12)
Very interesting! I wonder what that would look like
Right now, roughly, the algorithm recursively divides the image by doing decimation (ie. picking every other pixel), and keeps the decimated pixels as a second image
Not sure how that algorithm would apply to a 3d data structure
Do you know how 3d objects/images are usually represented?
It would be cool to recursively decompose a 3d object into smaller versions of itself :)
> Deciding to delegate to a future version of me that knows more math
Relatable. Huge part of my decision on what degree to pursue was a list of problems (mostly linear algebra) I needed to solve, but didn't have the guidance (and internet connection) to.
Well written! Would you mind sharing how you came up with the "middle out" numbering system? I can never seem to come up with something this inspired when I'm doing math problems by myself.
The post presents it a bit out of order, but it was mostly from realizing at some point that the way the fractal grows by a factor of 5, base 5 number systems, and the "spiral" mentioned in the post can all fit together. I also thought a lot about how to programmatically draw the fractal and a natural way would be to start from the middle and zoom out.
There's an apocryphal story about Richard Feynman about how he used to keep a dozen or so random problems in the back of his mind and made a little bit of progress on them every time he saw a connection, until finally he'd solve one and everyone would think he magically figured it out instantly. This was a bit similar except I'm not nearly at that level and I've only been able to do that for one problem instead of a dozen.
Yeah, maybe it is. It would be cool to make it much bigger, frame it and put it on the wall. Or create a mosaic tiled artwork, similar to Knuth’s dragon curve wall.
Yeah, it's in the last image and in the thumbnail at very top (which I realize now is really hard to spot on mobile), intentionally not in the spotlight to leave space for the twist at the end.
I think it would work perfectly as a mosaic eventually, but for the time being I'm perfectly content with the "rustic" 8x11 graph paper sized one taped to the wall. Currently planning to put up a slice of the orthotopeflower as a companion piece once I find matches for the colored pencils I used back then.
The the arms of the author's "wallflower" fractal don't seem to curve, as opposed to the other, similar fractal (quadratic von Koch island). Which can be explained by each iteration adding a mirroring.
The unfortunate thing here is that the swastika was appropriated by a genocidal regime. The symbol still has a totally different life in India and Japan.
It's an ingroup joke but also a true warning: "Handwaving" Anyone who delves deeply into something reaches a part where they can't articulate a developing theory and hand-wave around it -- hoping you "get" it.
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