[HN Gopher] That fractal that's been up on my wall for 12 years
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       That fractal that's been up on my wall for 12 years
        
       Author : chriskw
       Score  : 242 points
       Date   : 2025-05-22 15:50 UTC (7 hours ago)
        
 (HTM) web link (chriskw.xyz)
 (TXT) w3m dump (chriskw.xyz)
        
       | taeric wrote:
       | 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!
        
       | CBLT wrote:
       | 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.
        
         | chriskw wrote:
         | 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.
        
       | leni536 wrote:
       | 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.
        
       | entropicdrifter wrote:
       | Kinda looks like a propeller
        
         | shermantanktop wrote:
         | Things with four arms that all curve the same way unfortunately
         | tend to look swastika-ish.
        
           | leni536 wrote:
           | 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.
        
       | bdamm wrote:
       | That was fun.
        
       | nico wrote:
       | 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
        
         | Iwan-Zotow wrote:
         | Curious if it would work in 3D
        
           | nico wrote:
           | 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 :)
        
       | Scene_Cast2 wrote:
       | I wonder if something similar can be applied to get a dither
       | pattern with built-in level of detail adjustment.
        
       | cess11 wrote:
       | Nice writeup. The Heighway dragon of Jurassic Park fame is pretty
       | neat too.
       | 
       | https://en.m.wikipedia.org/wiki/Dragon_curve
        
       | CliffStoll wrote:
       | Outstanding work and a delightful read.
        
         | chriskw wrote:
         | 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 :)
        
       | tcshit wrote:
       | 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.
        
         | leephillips wrote:
         | Isn't that it on the left in the last image?
        
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       (page generated 2025-05-22 23:00 UTC)