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...]
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.
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.
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.
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.
> 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.
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.
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.
[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...]