#hilbert curve

[botherbug]

space filling curves. source.

[lesbianslovebts]

This is the 5th iteration of the Hilbert curve, which is a space-filling line fractal with Hausdorff dimension 2. I used 961 miyuki 11/0 delica beads, and it took me about 10-12 hours to make across multiple sessions. Feel free to reblog so people know math is beautiful!

[blake447]

So adding on to the work i've been doing with integer sequences that generate fravtal curves, we have the hilbert curve, which ends up a bit more... Complicated than some of the others

So we start with our usual set up. Each number represents an absolute heading we wish to travel, and we start with a generating shape. What we are going to do is try to fold segments of the loop inward to create the shape everyone associates with the hilbert curve

In this case we start with 103. Now we start with a sequence detection. Basically we're looking for triples of ascending or descending order mod 4. When we find them, we expand them by a factor of five, since thats how many segments the hilbert curve will have on that edge.

After that we decide which segments to replace. In this case its always the same, first non consecutive pair, last non consecutive pair, and the one dead in the middle of the middle segment.

What we replace them with is whatever pushes the segment between the two paired numbers into the inside of the loop, and we can do that by referencing the other directions in that loop like so. The first and last non consecutive pairs reference the middle direction and its opposite, and the middle non consecutive pair references the start and end direction. Note we can rotate something 180 degrees by adding 2 to it (mod 4)

Here is the process in code

And here is the result! I've never quite liked the regularity of the hilbert curve, but I wanted to tackle it because I've already done a fair amount of work with other curves, so i didn't want to exclude this one!

[wouldyourfavepaychildsupport]

Would the Hilbert curve pay child support?

[skadream]

heres a bunch o drawings of space filling curves over the years

heres a selfie from like 2015 w some dragon curves in the bg. i can probably find more in my box of old sketchbooks n shit

[heliotropopause]

gotta love a good space-filling curve.

[fractangle]

me earlier: my hand hurts

me a bit less earlier: i should try sashiko

me now: oughaghuhgh

i may be stupid

[salamencerobot]

Boss makes a dollar I make a dime

So I fuck around in Paint on company time

[s-lycopersicum]

Cursed to be the lone appreciator of the true beauty Hilbert curve, which is not in the rendered curves themselves, but on the intricate transformation of a number into a two-dimensional coordinate, and back again. The equilibrium in the numerical bases. The symmetry in the state transitions. Truly...

(↑ Lost in abstract delusions, please ignore.)

[dykeseinfeld]

things i do for this tár project: cold emailing a world-famous anthropologist bc i've been reading a book from the 80s on shepibo konibo pottery and it still didn't ahve what i needed and all i found a note in the citations that the museum he works for has some non-display pottery in its collection and all i need is to talk to literally one person who has done work on the significance and symbolism of the pattern carved into it

[kaznar342]

self-soothing activity of the day: drawing fractals.

specifically the hilbert's curve. again.

[lesbianslovebts]

My next bead project will be the fifth iteration of the Hilbert curve! ☺️

[blake447]

Please enjoy this failed attempt at making a hilbert curve, which I would like to call a hilbert planter! Basically we got some sign error stuff going on. A bit more study is needed to find some greater pattern to the original fractal, but until then I kind of like this one's appearance

Here's the snippet of code to iterate this sequence. Won't elaborate much further, check out my posts on dragon curves and sierpinski curves for more info, its similar to those.

And one more at the next iteration

[typecasto]

i too am plagued by visions (unable to sleep cause an algorithm popped into my head fully formed and i needed to write it down)

[capnsoapy]

the hilbert curve but it's a trans woman on [tumblr]

[tpwrtrmnky]

diehard

[ID: Three panel comic with crudely drawn stick people

Panel 1: A blue person and a crimson person are sitting at a table next to each other, talking.

Blue: "Look, the story arcs are just like that okay. They get really long and hard to follow to a point where only the diehard fans know what's going on, at least on a first watch."

Crimson: "It's a show that's only really for its established audience, kinda. People complain about the rambling drawn-out dialogues but that's sort of just what the show is about, for example?"

Blue: "Yeah I mean you sort of have to be into obtuse nonsense to get anything from the Hilbert Space Arc. What's that even about?"

Panel 2: Focus on a gold person, hunched over.

Gold: "There is no point to attempting to analyse the Hilbert Space Arc. It can't be done.

It's by far the worst arc in Vectorhetoric, specifically because it makes no sense. There is absolutely no way to make Gaussian curves map onto colours.

'spectral decomposition' is just nonsense words from evil websites.

And there is certainly no colour you could map onto the fucking spinors without being horrendously offensive by saying everyone with that colour is a violent revolutionary."

Panel 3: Zoom on a person who is yellow on the left and blue on the right.

Blue-Yellow: "Right. So hear me out.

I suspect, and to be clear this isn't based on a deep lore argument, just a hunch

I think 'the spinors are revolutionaries'

Might just be a pun."

End ID.]

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