would be nice if the lines were semitransparent and built up to white. The glare in the centre would be less then and make more pattern

At 120° my jaw dropped.

I did this once. Took a rather reasonable curve and ran through all the angles it could have had. There's more than a few others that are really amazing. Like some of the curves you run through hit other fractals that you wouldn't have considered simply with a different angle. It's pretty interesting as far as such things go. That said, the title is misleading there are more fractals dragons than just HH and clearly at other angles it's not a dragon. So this isn't all dragon curves, just all angles of the HH dragon curve.

The curve is made by, as you says, hooking on an exactly copy of the current curve, but rotated 90 degrees. Here is the algorithm that I wrote in matlab: d = [0 1]; % initiation for k = 1:18, d = [d fliplr(d)*exp(-1j*a)]; % a: folding angle end c = cumsum(d); % convert to complex coordinates Only three lines of (operative) code! (Coordinates located as complex numbers in the vector c). By letting a go from 0 to 2pi, the folding angle is increased.

Thanks! I'll take this into full consideration when I start recording for the album later this summer!

Haha! Thank you! I'm glad you enjoyed my music so much! I'm hoping to release an album of it this summer.

It would be interesting to see this with the angle set at 90, but the proportions of the fold changing.

Yes! I like that one too. When the fold angle is 120 degrees. The other one I like the bit from 1:04 onwards

I really hope you are a millionaire man! You have made my life richer these past 2 hours with your music!

My only complaint about your music is that it doesn't just go on for hours on end, I fall asleep to your music. If you go on to make an album, which I sincerely hope you do, please make the songs last longer. I could never tire of listening to such beautiful music.

This is absolutely remarkable.

I'd never heard of it before the Numberphile video a few weeks ago - it's really cool!

1:06 awesome line

It's really beautiful Thanks

You need to extend this by using different folding schemes. For example, if the paper is folded in 3 parts, in a "Z fold", the curve becomes interesting for a 120 degree angle. If the paper is folded into 3 parts, in a "U fold", the curve becomes interesting when the angle is 60 degrees.

Thats beautiful

nice approach to dragon curve, thinking longitude as constant pop corn head explotion

Why is it kinda pulsating sometimes? Are you fitting each frame into a square?

beautiful music!

I really like the piano backdrop, but I can't help but wonder if it would sound better on hang drum.

I started making instrumental music like this last Autumn but I've been writing songs and such like for years.

The Dragon Curve is like something Carl Sagan would come up with, like his alien message hidden in pi, only its real.

I'd love to see a video with the zoom level shown, I think that would be quite interesting to watch too!

do you think you could do the same type of thing with the Hilbert curve?

presumably, the animation is done via the corresponding Lindenmayer- or L-system? If you like those, you might want to check out other L-systems. There are some really amazing ones out there. Nice work! :)

nice song, matched really well the animation. beautiful. keep up the good work!

Thanks for watching!

after a while it gets rly trippy

Truly inspiring. Thanks

Beautiful

Thanks, that was beautiful!

Damn, I was watching this and when it finished I looked somewhere else on my screen, it seemed like the KZfaq interface was twisting.

Hey Alan, I was wondering where is the music you made for the Numberphile video about Good Will Hunting? The music was amazing.

44: *triangles.*

Thank you so much for this.

Paper divided by zero.

I love 120° and 240°

Alan Stewart's song reminds me of Alan Parson's Turn of a Friendly Card.

1:09

Beautiful!

1:06 is it's midway point in case anyone wanted to know:)

How long have you been composing like this?

Everything after 180 degrees is just a mirror image of before 180 degrees

Obviosly optimal at 90°, but really awesome otherwise

I'll send you a PM with a download link for the GWH music. I haven't uploaded a video for that as it was so short.

Theres more?

Am I the only one who saw the optical illusion after watching the video? Everything was rotating

So, 0°=180°=360°, and 90°=270°? (I’m only in 6th grade)

0.33 right dragon curve!

Great animation! Would you be willing to share the code?

At 120 deg it just becomes triangles

Alan, sorry to bother, but I too would love to get the download link for the GWH music. Cheers!

Trippy😌😌😌😳

Spirograph.

wow

Great!....

How many "folds" are there?

Hey man, no bother at all! I've sent you a link in a PM

This is literally the type of thing I see on drugs

Dreidel

What did I just watch, exactly?

LET ME SLEEP

Really not that helpful to keep rotating the whole thing. Just keep the two main points static. Then upload that.

I think your work shows that something original begins to happen to you. Congratulations. I hope I can see a performance live yours someday. I am attaching the link of an artist website that may be interesting for you. For me it is a contemporary reference for their work and an old friend. fredericamat. net/ en / films