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 :)
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 :)
That's really cool! I tried to get something to work last week on pen and paper but couldn't get anything to stick. Is there a strategy you used or did you just go by feel?
Edit: just noticed how you encoded a flip (AB <--> CD) between iterations like how the matrix flips the orientation of space. Super neat!
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!
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.
[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)
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.
Readit News
Loved the 3d visualizations
It reminds me of this thing I built some time ago while playing with recursive decimation to generate effects similar to fractals from any image
You can play with it here: https://jsfiddle.net/nicobrenner/a1t869qf/
Just press Blursort 2x2 a couple of times to generate a few frames and then click Animate
You can also copy/paste images into it
There’s no backend, it all just runs on the browser
Don’t recommend it on mobile
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 :)
https://onlinetools.com/math/l-system-generator?draw=AB&skip...
edit: On second thought, this probably generates the other fractal, but I'm not sure.
https://onlinetools.com/math/l-system-generator?draw=ABCD&sk...
The previous one fills out the Koch island.
Edit: just noticed how you encoded a flip (AB <--> CD) between iterations like how the matrix flips the orientation of space. Super neat!
Question to the author: what would you recommend to hang on my kid’s wall today?
I expect 41+14 to be 12 (two right plus two up equals two right and two up).
Long addition in long form below uses:
'=' to show equivalent lines (reordering of terms (1+2=2+1), spliting numbers (41=40+1), adding single digits (1+4=22))
'->' for when the algorithm gives a digit
'<' for when we move over a column
[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)
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.
https://raw.githubusercontent.com/cies/haskell-fractal/refs/... [17MB, sorry Github]
It contains the Haskell code that produced it: https://github.com/cies/haskell-fractal
Especially the `sharpen` function was interesting to come up with (I used some now-offline tool to do curve fitting for me): https://github.com/cies/haskell-fractal/blob/master/fractal....
Fun little project. :)