Outstanding work and a delightful read.

This is so much better than reading the news.

Favorited—I'll be coming back to absorb more, as my aging semi-fluency in engineering physics and SQL doesn't help much with the notation I last saw in the 1980s.

Amazing insightful and thoughtful write up, thank you!

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

Thought I'd check the arithmetic for 2 two-digit numbers, and it works!

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

    41+14
    = (40+1)+(10+4)
    = 40 + 10 + (1+4)
    = 40 + 10 + 22
    -> 1s digit = 2
    < 4 + 1 + 2
    = 22 + 2
    = 20 + 2 + 2
    = 20 + 41
    -> 10s digit = 1
    < 2 + 4
    = 0
    -> done
    == 12

It still works in the alternative system (14+21 should equal 12)

    14+21
    =10+20+42
    ->2
    <1+2+4
    =13+4
    =10+3+4
    =10+31
    ->1
    <1+3
    =0
    ==12

This went much deeper and harder than expected. One has to admire the dedication.

Question to the author: what would you recommend to hang on my kid’s wall today?

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!

> 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.

Got a bit nerd-sniped by this and came up with an L-system that fills out (I think) "the wallflower":

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.

Nice writeup! I was hoping to see a photo of the fractal on your wall.. Nice link to Knuth video that I somehow have missed.

This is beautiful. Thank you.

well, that escalated beautifully

I wonder if something similar can be applied to get a dither pattern with built-in level of detail adjustment.

Nice writeup. The Heighway dragon of Jurassic Park fame is pretty neat too.

https://en.m.wikipedia.org/wiki/Dragon_curve

I had this one up the wall (giant print) at a place I worked:

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. :)

Kinda looks like a propeller

That was fun.

Now make a tiling game engine that uses these!

Too much math.