H Fractal.

[swestrup]

I just 'invented' a closed plane-filling fractal that I don't recognize. I tried to Google for it, but I didn't have much luck with finding closed fractal curves on square grids. Anyway, I wrote up a blurb about it on my website (where I have a bit more control over rendering than I do here).

Forgive the crappy ASCII art, but I wasn't willing to go to too much extended effort if it turns out that this is Horgledorf's Curve and everyone has known about it for ages.

Comments

[cpirate.livejournal.com]

I don't know about that curve in particular, but see XKCD, of all places, for something a bit similar. He talked about it a bit more in his blog (er, blag).

[swestrup]

Actually, that's where I started. I looked up the properties of that curve, and what it was good for, and started reading up on a large number of fractal curves. At some point I decided (for reasons I no longer recall) that it would be better for some applications to have a similar one that was closed-loop. I did some looking around, but never found any.

Then last night the curve I pointed to occurred to me.

[cpirate.livejournal.com]

Ah, right, the closed loop thing. In that case I've got nothing.

It's good to know that we started from the same place though, my head might have exploded a bit if it had just happened to be synchronicity.

[kallisti.livejournal.com]

If you don't already have it, grab a copy of fractint, as it has built in many, many dozens of fractals, and may have the one you are looking at...and if not, it references lots of sources for information on fractals.

http://spanky.triumf.ca/www/fractint/FRACTINT.HTML

ttyl
Farrell

[swestrup]

I used to play around with Fractint a lot, but I haven't looked at it in over a decade. Maybe its time I did, again.

[tjernobyl.livejournal.com]

You may find that rendering is somewhat quicker than before...