#hilbert curve

[sevenfromelevenisfour]

I love french knots, and needed a gauge swatch to estimate how much thread I'll need and how many knots it takes to fill a given area. I figured the most effective way to fill in a space with a distinctive pattern was my favorite space filling curve:

I was originally going to fill in the spaces between the lines with a contrasting color, but it looked so good as is I decided to leave it.

Now, this didn't really give me as good of an estimate as I wanted, so I made another swatch of the Ulam Spiral

I goofed up and marked one as prime, but I don't know how to fix that stitch without undoing a lot of work so ¯\_(ツ)_/¯. It ended up a 20x20 grid covering numbers 1 to 400.

I'll probably end up using these as pockets or patches on another project. I also did a bigger piece using some variegated thread of the letter phi since it represents my favorite ratio.

[hyrodium]

I made a Multi-layered maze inspired by Hilbert curve.

[fruityfishs0up]

"Maybe I can understand why the number 4 could be terrifying to some folks, but for me, it's a comfort."

End of the Dream as the Hilbert curve.

[wathav]

Did you know gifs aren't limited to 256 colours? Sick and tired of seeing grainy, washed out fandom gifs?

[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!

[watam]

Aaaaand the 8 state 2n-2 solution to the Synchronization Problem has been recoloured and mapped to Hilbert curves and a linear back and forth path

[botherbug]

space filling curves. source.

[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!