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The golden ratio has spawned a beautiful new curve: the Harriss spiral

157 points by bootload 12y ago

lubujackson 12y ago
This isn't remotely new information?
- DanBC 12y ago
  Where has the Harriss spiral appeared before?
jbob2000 12y ago
"Duuude, what if instead of cutting a square, we cut a rectangle?" "No way maaann! Unheard of!"
- DanielStraight 12y ago
  You mock, but this kind of tinkering is basically the foundation of mathematics. I suggest reading Lockhart's Lament, linked on this Wikipedia page: https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament Relevant quote: > For example, if I’m in the mood to think about shapes— and I often am— I might imagine a triangle inside a rectangular box. I wonder how much of the box the triangle takes up? Two-thirds maybe? The important thing to understand is that I’m not talking about this drawing of a triangle in a box. Nor am I talking about some metal triangle forming part of a girder system for a bridge. There’s no ulterior practical purpose here. I’m just playing. That’s what math is— wondering, playing, amusing yourself with your imagination.
  - Udo 12y ago
    Aside from its style, this seems like a valid criticism. How trivial can a permutation be and still be sufficiently interesting for someone to (justifiably) slap his name on it? That said, this was still a nice read and the guy is obviously having fun with it, so good for him.
    - Gelada 12y ago
      In this case the change is significant. If you just cut squares you can do quite a bit and it leads to significant ideas related to continued fractions, but you will only get finite continued fractions (rational numbers) and periodic ones (quadratic numbers). Cutting rectangles and squares can give higher degree algebraic numbers, like the cubic number for the main spiral. I am working on a porrf that you can get all algebraic numbers.
T-hawk 12y ago
Why do we delete the largest arc? I couldn't understand the elegance of the spiral until seeing that that had been done. Deleting that largest arc breaks the self-similarity. Without it, the topmost scale becomes an S curve and doesn't match the smaller layers of branching curves. I looked at the first image for around a minute trying to find the S curves in the lower layers to establish the self-similarity.
- zem 12y ago
  i like it - it looks more plantlike with the largest arc deleted
dudifordMann 12y ago
So... he applied an L-system to a Fibonacci -spiral? I suppose that's innovative.
- theoh 12y ago
  Like with the endless fractal images from the '90s, it takes a certain kind of blinkered idea of aesthetics to get excited about this. At least the Mandelbrot set was mysterious and surprising.
- ajkjk 12y ago
  I don't understand this kind of dismissal. So what if he did? Maybe the innovation is considering this kind of thing as art again when it's passe.
CapitalistCartr 12y ago
It looks very Dr. Seuss.
proee 12y ago
We have some ferns in our yard that have similar curves. Curious to know what other nature forms take this on. https://s-media-cache-ak0.pinimg.com/236x/9d/0a/36/9d0a365fda002822f2ca8359bae6fc9a.jpg https://s-media-cache-ak0.pinimg.com/236x/9d/0a/36/9d0a365fd...
- HCIdivision17 12y ago
  That's a really spiffy connection you found. I wonder what modification to the Harriss curve is needed to make it so that it only curves inward? (I had been hoping to see if he goes more in-depth on the process, but his site's sorta dying). It might be entertaining to fool with it a bit in Processing and see what comes out.
- dima55 12y ago
  It's this: http://en.wikipedia.org/wiki/Fiddlehead http://en.wikipedia.org/wiki/Fiddlehead
pcrh 12y ago
Some are uncannily similar to Celtic knots.
Chinjut 12y ago
As a mathematician, I was all ready to be dismayed by or dismissive of the article, as with almost all popular discussion of mathematics (and particularly so with the reams of nonsense which have been written in the past about "the golden ratio"), but I was pleasantly surprised to find it reasonably well written and interesting. Hoorah! [I do wish it hadn't linked at the end to this twaddle about the golden ratio governing women's peak fertility through their uterus dimensions...]
boyaka 12y ago
Made me think of the trisquel logo, although that is apparently related to many other historical symbols and is probably less math and more design. http://trisquel.info/en/wiki/logo http://trisquel.info/en/wiki/logo
arjn 12y ago
Very interesting and pretty ... and it does remind me of Celtic art.
drcode 12y ago
Hmm... I have to say, I'm a little underwhelmed by both the aesthetics and the technical construction of this particular curve, but who am I to complain about the aesthetics of another man's fractal.
dynofuz 12y ago
Ugh makes me want to ralph
chii 12y ago
it looks surprisingly similar to a dragon curve

157 points by bootload 12y ago

lubujackson 12y ago

This isn't remotely new information?

DanBC 12y ago
Where has the Harriss spiral appeared before?

jbob2000 12y ago

"Duuude, what if instead of cutting a square, we cut a rectangle?" "No way maaann! Unheard of!"

DanielStraight 12y ago
You mock, but this kind of tinkering is basically the foundation of mathematics. I suggest reading Lockhart's Lament, linked on this Wikipedia page: https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament Relevant quote: > For example, if I’m in the mood to think about shapes— and I often am— I might imagine a triangle inside a rectangular box. I wonder how much of the box the triangle takes up? Two-thirds maybe? The important thing to understand is that I’m not talking about this drawing of a triangle in a box. Nor am I talking about some metal triangle forming part of a girder system for a bridge. There’s no ulterior practical purpose here. I’m just playing. That’s what math is— wondering, playing, amusing yourself with your imagination.
- Udo 12y ago
  Aside from its style, this seems like a valid criticism. How trivial can a permutation be and still be sufficiently interesting for someone to (justifiably) slap his name on it? That said, this was still a nice read and the guy is obviously having fun with it, so good for him.
  - Gelada 12y ago
    In this case the change is significant. If you just cut squares you can do quite a bit and it leads to significant ideas related to continued fractions, but you will only get finite continued fractions (rational numbers) and periodic ones (quadratic numbers). Cutting rectangles and squares can give higher degree algebraic numbers, like the cubic number for the main spiral. I am working on a porrf that you can get all algebraic numbers.

T-hawk 12y ago

Why do we delete the largest arc? I couldn't understand the elegance of the spiral until seeing that that had been done. Deleting that largest arc breaks the self-similarity. Without it, the topmost scale becomes an S curve and doesn't match the smaller layers of branching curves. I looked at the first image for around a minute trying to find the S curves in the lower layers to establish the self-similarity.

zem 12y ago
i like it - it looks more plantlike with the largest arc deleted

dudifordMann 12y ago

So... he applied an L-system to a Fibonacci -spiral? I suppose that's innovative.

theoh 12y ago
Like with the endless fractal images from the '90s, it takes a certain kind of blinkered idea of aesthetics to get excited about this. At least the Mandelbrot set was mysterious and surprising.
ajkjk 12y ago
I don't understand this kind of dismissal. So what if he did? Maybe the innovation is considering this kind of thing as art again when it's passe.

CapitalistCartr 12y ago

It looks very Dr. Seuss.

proee 12y ago

We have some ferns in our yard that have similar curves. Curious to know what other nature forms take this on. https://s-media-cache-ak0.pinimg.com/236x/9d/0a/36/9d0a365fda002822f2ca8359bae6fc9a.jpg https://s-media-cache-ak0.pinimg.com/236x/9d/0a/36/9d0a365fd...

HCIdivision17 12y ago
That's a really spiffy connection you found. I wonder what modification to the Harriss curve is needed to make it so that it only curves inward? (I had been hoping to see if he goes more in-depth on the process, but his site's sorta dying). It might be entertaining to fool with it a bit in Processing and see what comes out.
dima55 12y ago
It's this: http://en.wikipedia.org/wiki/Fiddlehead http://en.wikipedia.org/wiki/Fiddlehead

pcrh 12y ago

Some are uncannily similar to Celtic knots.

Chinjut 12y ago

As a mathematician, I was all ready to be dismayed by or dismissive of the article, as with almost all popular discussion of mathematics (and particularly so with the reams of nonsense which have been written in the past about "the golden ratio"), but I was pleasantly surprised to find it reasonably well written and interesting. Hoorah! [I do wish it hadn't linked at the end to this twaddle about the golden ratio governing women's peak fertility through their uterus dimensions...]

boyaka 12y ago

Made me think of the trisquel logo, although that is apparently related to many other historical symbols and is probably less math and more design. http://trisquel.info/en/wiki/logo http://trisquel.info/en/wiki/logo

arjn 12y ago

Very interesting and pretty ... and it does remind me of Celtic art.

drcode 12y ago

Hmm... I have to say, I'm a little underwhelmed by both the aesthetics and the technical construction of this particular curve, but who am I to complain about the aesthetics of another man's fractal.

dynofuz 12y ago

Ugh makes me want to ralph

chii 12y ago

it looks surprisingly similar to a dragon curve