# Talk:Doyle spiral

This review is transcluded from Talk:Doyle spiral/GA1. The edit link for this section can be used to add comments to the review.
Reviewer: Duckmather (talk · contribs) 03:34, 24 June 2022 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
Pretty well done, although it's short.
It is reasonably well written.
a (prose, spelling, and grammar):  b (MoS for lead, layout, word choice, fiction, and lists): 
Overall I think this article is well-written and understandable - no grammar errors pop out at me. The lead section is okay, though short. The layout and wording are fine. Minor opinionated nitpicks:
Link the word mathematics in the lead sentence or get rid of it altogether.
I don't think so. It is important to mention that the article is about mathematics, because readers might not recognize that from the more technical phrase "circle packing" also used to provide context. But MOS:OVERLINK warns us not to link "Everyday words understood by most readers in context (e.g., education, violence, aircraft, river)". I think mathematics is at the same level as those words. —David Eppstein (talk) 07:11, 24 June 2022 (UTC)
in the late 1980s or early 1990s should be something like in the late 1980s and early 1990s (emphasis mine, don't actually put it in), as this reads like an expression of doubt.
But it is an expression of doubt. As the references state more precisely and clearly, the first published appearance of Doyle's contributions is in a paper by someone else, in 1992 and another paper by yet another group of non-Doyles in 1994. The 1992 paper refers to them as "Peter Doyle's unpublished ideas" and cites an undated "oral communication" by Doyle. The 1994 paper refers to "a fascinating observation of Peter Doyle" without citation. Based on these references, it is impossible to narrow down the timeframe of Doyle's contributions any more precisely. Note that MOS:DOUBT does not prohibit any wording; it merely says to be careful using some kinds of wording. But in this case the wording in question is not the kind of biased expression of doubt, introducing an editorial opinion in a backhanded way, that MOS:DOUBT warns against. It is merely an accurate representation of the knowledge that can or in this case cannot be gleaned from the sources.  —David Eppstein (talk) 07:11, 24 June 2022 (UTC)
OK, maybe rephrase this as {{tq|around the early 1990s}} (which is what your summary of the refs seems to indicate). Duckmather (talk) 20:59, 5 July 2022 (UTC)
For more, see Fermat's spiral § The golden ratio and the golden angle. should be replaced with a See also section or {{see also}} instance that links to Fermat's spiral#The golden ratio and the golden angle, because the current way is a bit clickbait-y.
This is not deserving of its own section and see-also section header link, but it is too central to the phyllotaxis application to separate it from the application section and provide only a bare link in a see-also section, stripped of its context. I think the current full paragraph length is the correct amount of content to devote to this related topic. —David Eppstein (talk) 07:48, 24 June 2022 (UTC)
Update: As part of some other copyedits, I found a way to work the "for more" link into the main text of the paragraph, instead of having a separate "for more" sentence. —David Eppstein (talk) 18:35, 26 June 2022 (UTC)
Each four consecutive circles should be Every four consecutive circles.
I'm not convinced this makes any difference in grammatical correctness or meaning, but it's harmless enough; done. —David Eppstein (talk) 07:44, 24 June 2022 (UTC)
An example can be seen in the stained glass church window shown, of type (8,8). contradicts the stained glass window's caption, which claims that the window represents a Doyle spiral of type (9, 9), in addition to being slightly awkwardly phrased.
Typo, fixed, thanks for catching. Also copyedited. —David Eppstein (talk) 07:17, 24 June 2022 (UTC)
It is factually accurate and verifiable.
a (reference section):  b (citations to reliable sources):  c (OR):  d (copyvio and plagiarism): 
Each source looks reliable at first glance (ref #2 is a bit nonstandard, but I won't complain), and ~everything is cited somewhere so I don't think we need to worry about OR. I can't see most of them because of paywalls and such, but I've checked a few:
Ref #1 should really only cite page 455, since the other pages don't discuss this spiral at all.
Correct citation style for journal or magazine articles is to cite the entire range of pages of the article. Our citation templates do not provide the means to correctly cite the place where an article appears (its journal or magazine, date, range of pages, etc.) and to also cite any specific location within that article. We can point to pages or ranges of pages within book citations, but not within articles. (Do not tell me about {{rp}}. It is an abomination.) —David Eppstein (talk) 07:19, 24 June 2022 (UTC)
Ref #3 should also only cite pages 119–122. Also it only seems to discuss the geometry of the spiral,
Ditto. —David Eppstein (talk) 07:19, 24 June 2022 (UTC)
Ref #6 is dense and I can't quite see how it supports some of the statements that cite it, but no obvious mistakes.
(Also, No copyvio issues.)

It is broad in its coverage.
a (major aspects):  b (focused): 
Again, the article is short (if I weren't doing this good article review I would probably rate it as C-class), but it does a good job of staying on topic. The Doyle spirals form a discrete analogue of the exponential function, as part of the more general use of circle packings as discrete analogues of conformal maps. needs a bit more explanation, though, since it's unintuitive/not obvious.
You did notice the immediately following sentence, that if you apply the exponential function to a regular hexagonal packing you get something that looks a lot like the Doyle tiling? It was intended as the explanation for this analogy. There's a more detailed explanation of the same analogy at Circle packing theorem#Relations with conformal mapping theory (bearing in mind that the exponential function is an example of a conformal map). Do you think it would be helpful to provide another see-also type link there, like the one for the Fermat spiral unit circle packing phyllotaxis model? —David Eppstein (talk) 07:52, 24 June 2022 (UTC)
I found more on this in another source and added another sentence linking the Doyle spiral to the exponential map by an analogy involving the radius-ratio parameters and Schwarzian derivative. —David Eppstein (talk) 07:42, 26 June 2022 (UTC)
It follows the neutral point of view policy.
Fair representation without bias: 
No problems here (one of the benefits of writing about math IMHO!)
It is stable.
No edit wars, etc.: 
No problems here (User:David Eppstein wrote the vast majority of this, but whatever \shrug)
It is illustrated by images and other media, where possible and appropriate.
a (images are tagged and non-free content have non-free use rationales):  b (appropriate use with suitable captions): 
No problems here
Overall:
Pass/Fail: 
Overall I'd support this as a good article, though this warrants another opinion.
←=== Some comments from Ovinus ===
To provide a second opinion:

Any reason to link circle packing to circle packing theorem instead of just circle packing? Ovinus (talk) 06:15, 26 June 2022 (UTC)
I hadn't thought carefully about that, but I think circle packing theorem is the better link. The reason is that circle packing theorem is specifically about the combinatorial patterns of tangent circles in the plane, of arbitrary and varying sizes, leaving gaps surrounded by exactly three circles. On the other hand, circle packing is more focused on how densely one can pack unit circles into given shapes, and much less about the pattern of tangencies of the circles. —David Eppstein (talk) 07:16, 26 June 2022 (UTC)
Sounds good. It’s interesting how those articles are named. Ovinus (talk) 15:48, 26 June 2022 (UTC)
Is there an isomorphism of graphs between any two Doyle spirals? Ovinus (talk) 06:15, 26 June 2022 (UTC)
Never. You can count the arms by looking only at the graph, and the different arm counts show that Doyle spirals with different parameters always have different graphs. I don't know of a source explicitly saying they're always non-isomorphic as graphs, though. —David Eppstein (talk) 07:16, 26 June 2022 (UTC)
Yeah that’s what I’d surmised (both that they weren’t ever isomorphic and that there’d be no sources) Ovinus (talk) 15:48, 26 June 2022 (UTC)
"uniquely up to scaling and rotation" link to "similarity"? Maybe that's a bit of an easter egg Ovinus (talk) 06:15, 26 June 2022 (UTC)
Ok, changed to "up to similarity". —David Eppstein (talk) 07:16, 26 June 2022 (UTC)
"have symmetries that combine scaling and rotation around the central point" Cool, but what is the actual group structure? (Needn't be too much in depth, but for example, what degree rotational symmetry does it have?) Ovinus (talk) 06:15, 26 June 2022 (UTC)
It's a discrete subgroup of the multiplicative group of complex numbers. It has the graph of the spiral as a Cayley graph (with a redundant set of generators that step along all three spiral arms). But our main source on its symmetries (Bobenko and Hoffmann) doesn't seem to say any of this. The discrete subgroup of complex part is briefly mentioned at web page https://www.science.smith.edu/phyllo/About/Lattices/SpiralLattices.html but I'm skeptical that it's a reliable source, especially because it doesn't carefully distinguish between Doyle spirals and Fermat spirals. —David Eppstein (talk) 07:39, 26 June 2022 (UTC)
Understood. That’s sad there isn’t an RS for that Ovinus (talk) 15:48, 26 June 2022 (UTC)
I did find a paper classifying these discrete subgroups, but unfortunately without any mention of their connection to Doyle spirals: Mihaila, Ioana (2006), "Constructions of multiplicative-periodic functions on 
  
    
      
        
          
            C
          
          
            ∗
          
        
      
    
    {\displaystyle \mathbb {C} ^{*}}
  
", Complex Variables and Elliptic Equations, 51 (1): 1–7, doi:10.1080/02781070500323013, MR 2201252. —David Eppstein (talk) 18:53, 26 June 2022 (UTC)
Interesting. Alas I don't have access to that paper, but it makes sense that discrete infinite subgroups of 
  
    
      
        
          C
          
            ×
          
        
      
    
    {\displaystyle C^{\times }}
  
 would exhibit such a spiral pattern... Ovinus (talk) 03:53, 27 June 2022 (UTC)
"the space of realizations of locally-square spiral packings is infinite-dimensional" Why is "realizations of" necessary? You could say "space of... packings in the plane" if you want to be super explicit Ovinus (talk) 06:15, 26 June 2022 (UTC)
Removed. —David Eppstein (talk) 07:53, 26 June 2022 (UTC)
The Doyle spiral, in which the circle centers lie on logarithmic spirals and their radii increase geometrically in proportion to their distance from the central limit point, should be distinguished from a different spiral pattern of disjoint but non-tangent unit circles Why restate the Doyle spiral's logarithmic features when we don't mention Fermat's lack of them? I'd only contrast that the Doyle spiral has circles of varying radii, the most fundamental difference. Ovinus (talk) 06:15, 26 June 2022 (UTC)
I was trying to contrast both the logarithmic-spiral placement of the circles in the Doyle spiral with the Fermat-spiral placement in the other pattern, and the growth of the circles in the Doyle spiral with the fixed size of the circles in the other pattern. So they differ in two key ways, not just one: they place the circles on different shapes of spiral curves, and they change or don't change the sizes of the circles in different ways. Despite which there are sources that confuse them (see web link above). I'd welcome suggestions for other ways of making this point more clearly. —David Eppstein (talk) 07:56, 26 June 2022 (UTC)
Hm, fair enough to make that distinction. How about just separate it into two sentences for these two related points? The original was just a bit tedious. Ovinus (talk) 15:48, 26 June 2022 (UTC)
Copyedited. Better now? —David Eppstein (talk) 18:35, 26 June 2022 (UTC)
An enjoyable article. Ovinus (talk) 06:15, 26 June 2022 (UTC)

Oh also: the church window photo is pretty, but a little misleading. My understanding, perhaps faulty, is that the two rings are fine, but the middlemost circle bucks the pattern? I think this could be explained a bit better ("please ignore the middle circle!"). It'd be nice to have a clean example of a Doyle spiral in which all three families of spirals are nonlinear; the first image in the article has a linear family. Are there no nice such photos on Commons? Not a requirement for GA, but I could make some. Ovinus (talk) 06:28, 26 June 2022 (UTC)
That's why it says "the window's other circles do not follow the same pattern"; you think the same thing could be said more clearly? We do have an actual published source for the connection between spirals of circles and church rosette windows, the Fernández-Cabo reference; that was the best example I could find on commons but there is a huge number of rosette window photos there, not well categorized, so maybe there is another one that is more clear. We do actually already have, in the article, a "clean example of a Doyle spiral in which all three families of spirals are nonlinear": it's the Coxeter loxodromic sequence. But I don't know of any others on commons (see Commons:Category:Circle packings). If you can figure out a way to get a nice svg format image from the Doyle spiral explorer extlink, that might be a possibility. —David Eppstein (talk) 07:23, 26 June 2022 (UTC)
Yes I did see that but I would focus on excommunicating the middle circle because the outer circles don’t particularly matter anyway. Could be like “the window’s other circles, including the center one, do not follow the same pattern”. And yes, Coxeter’s sequence follows my criteria but is a bit extreme ;) I will make an SVG if/when I have time tonight (but again, not particularly relevant for GA). Ovinus (talk)
Ok, copyedited. —David Eppstein (talk) 18:35, 26 June 2022 (UTC)
Am quite happy with the current state of the article. Ovinus (talk) 03:53, 27 June 2022 (UTC)

@Duckmather: I think all issues discussed above have been addressed (and, separately, some nice images by Ovinus added to the article), so the ball is in your court for a decision on this nomination. —David Eppstein (talk) 19:45, 30 June 2022 (UTC)
Eh, might as well. (The images by Ovinus should go at the bottom of section Counting the arms and the gallery caption seems contradictory, but whatever.) Support. Duckmather (talk) 21:02, 5 July 2022 (UTC)
I think as the official reviewer you're supposed to actually take action rather than just making a vote. But now I'm curious: why the bottom of the section? WP:GALLERY doesn't seem to say anything about placement beyond "near the relevant text". The purpose of these images for me is to illustrate the first paragraph of that section, about how you count arms, which is why I put it after that paragraph. The other paragraph is elaboration on stuff you can do with arm counts that is not really specifically illustrated. And I also am confused what might be contradictory in the caption. —David Eppstein (talk) 21:12, 5 July 2022 (UTC)
@Duckmather: Friendly reminder.  Ovinus (talk) 08:16, 27 July 2022 (UTC)
@Duckmather: Hello? Do you intend to complete this review? —David Eppstein (talk) 03:21, 18 August 2022 (UTC)
It seems he's gone AWOL.... I think it's alright to IAR close it in a few days, given his support. Ovinus (talk) 05:42, 23 August 2022 (UTC)
Per the discussion at WT:GAN I'm going to pass this. Ovinus (talk) 04:55, 12 September 2022 (UTC)
Thanks for passing! I indeed totally forgot about this after completely botching the GA review closure. Duckmather (talk) 00:11, 13 December 2022 (UTC)

Back home, so I can work on some images. Here's a simple draft of a (7,8) spiral as an SVG with the seven spirals enumerated (I have created the same figure for the eight spirals and single spiral). Of course the program works with any reasonable (p,q). Suggestions on colors, different indications, etc.? Ovinus (talk) 05:39, 28 June 2022 (UTC)
Annoyingly, something seems to be removing or ignoring dominant-baseline="middle". Will fix. Ovinus (talk) 05:44, 28 June 2022 (UTC)

Looks pretty good. I like the idea of using numbers to clarify how the arms are counted. Maybe more contrasty colors for adjacent spirals, rather than trying to make them into a smooth gradient? Checking against an online color blindness simulator might also be a good idea. If you used a (6,8) spiral instead of (7,8) then it would be possible to make versions highlighting all three types of arms, and you would only need two colors to make all pairs of adjacent arms contrast, but with the one you chose, one of the arms contains all the circles making it difficult to highlight. I looked at recoloring your image so that most circles were neutrally colored and with overlapping bands of colors for a selected arm of each type (like the 1911 lead image, but in color and with multiple types of arms shown) but I didn't save and upload as I don't think it came out looking very good. —David Eppstein (talk) 07:21, 28 June 2022 (UTC)
Thoughts on these (could also be combined into a single GIF with links to the SVGs)?

According to [1] these color combinations (#000 text on (#3a3 or #77c) on #fff background) are accessible. Ovinus (talk) 19:15, 28 June 2022 (UTC)
I tried adding these to the article, more or less as presented above but with captions. —David Eppstein (talk) 20:05, 28 June 2022 (UTC)

I was curious about the Mobius transformations and decided to see what they actually look like. I admit this is screen recorded from my web app, as the shit video quality suggests. I was too lazy to properly convert to video, although I will eventually. There is also float precision annoyance that I must iron out. Essentially it just takes the transformation 
  
    
      
        z
        ↦
        
          
            z
            
              c
              z
              +
              1
            
          
        
      
    
    {\displaystyle z\mapsto {\frac {z}{cz+1}}}
  
 and lets 
  
    
      
        c
      
    
    {\displaystyle c}
  
 go from 0 to 0.5 or so. It clarifies a couple points I didn't really intuit after reading the passage. First, the result of a Mobius transformation on a Doyle spiral for which the preimage of complex infinity is inside a disc maps the disc to the complement of a disc, and thus doesn't result a circle packing at all. I suppose it's trivial now that I see it, but I had no clue before. Second, it is possible to have a circle packing for which each circle has six tangencies and those tangencies form a ring, but that is not a Doyle spiral, if the ring of tangencies is allowed to not enclose the circle (see ~0:25 in the video). Anyway, thought you might enjoy it. Ovinus (talk) 05:21, 3 July 2022 (UTC)

Not to inundate the article with images, but here's one I came up with to illustrate how the Mobius transformation works. The "inverted disc" phenomenon might be OR, so I just rendered this one. Ovinus (talk) 22:42, 5 July 2022 (UTC)
You can find images generated by a Möbius transform of a Doyle spiral, sort of like this one, in Wright's "Searching for the cusp". A tighter crop might help better show the way it spirals in to two points rather than one (the second spiral center is where the Möbius transform takes the point at infinity). —David Eppstein (talk) 04:40, 6 July 2022 (UTC)
Oh good. Yeah, I tried zooming in on the image. I could also make a square-ish one if that feels more shapely. Ovinus (talk) 13:34, 6 July 2022 (UTC)
In the caption, more specifically, it is the three outer circles that are not surrounded. —David Eppstein (talk) 14:37, 6 July 2022 (UTC)
Ye. Alright, added. Ovinus (talk) 07:54, 23 July 2022 (UTC)