Timeline for Is there a generalisation of the "sunflower spiral" to higher dimensions?
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| S Sep 7, 2017 at 1:41 | history | suggested | jeq | CC BY-SA 3.0 |
Copied image to imgur.com, as it was not being displayed because of the new https rule. Added link to original image source.
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| Sep 7, 2017 at 1:26 | review | Suggested edits | |||
| S Sep 7, 2017 at 1:41 | |||||
| Feb 18, 2016 at 15:36 | history | edited | user9072 |
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| Sep 27, 2010 at 20:15 | answer | added | Paul-Olivier Dehaye | timeline score: 1 | |
| Jul 1, 2010 at 4:57 | answer | added | user7234 | timeline score: 2 | |
| May 22, 2010 at 6:56 | answer | added | jeremy | timeline score: 2 | |
| May 22, 2010 at 5:49 | answer | added | DoubleJay | timeline score: 1 | |
| May 16, 2010 at 15:20 | answer | added | Tom Boardman | timeline score: 5 | |
| May 16, 2010 at 5:55 | comment | added | Henry Segerman | @Robby: J.N.Ridley, in "Packing efficiency in sunflower heads" shows that among patterns with $r(n) = \sqrt{n}$ and $\theta(n) = \lambda n$ for some $\lambda \in \mathbb{R}$, the sunflower spiral gives the most efficient packing pattern, meaning that the infimum of distances between nodes is maximised. The choice of $r(n) = \sqrt{n}$ is reasonable because it means that the ratio of the number of points in a circle centered at the origin to the area of that circle approaches a non zero finite limit as the radius goes to $\infty$. | |
| May 16, 2010 at 5:16 | answer | added | S. Carnahan♦ | timeline score: 7 | |
| May 16, 2010 at 3:42 | comment | added | Wadim Zudilin | @Henry: Thanks for details! If there is no obvious pattern, then it should be hard to design the packing "nicely". I have definitely never heard about 3D versions of the sunflower spiral. I may suggest you add your 3D experiments in the statement of problem next time you edit it. | |
| May 16, 2010 at 3:34 | comment | added | Henry Segerman | @Wadim: I also tried just getting a reasonable "packing sequence" on the sphere, by putting the next point of the sequence at the point furthest from all already chosen points of the sequence (using a Voronoi tile algorithm). This works to make a sequence, but it isn't some simple iteration and it looks random: no interesting patterns. | |
| May 16, 2010 at 3:34 | comment | added | Henry Segerman | @Wadim: Some time ago I tried choosing a sequence of points on $S^2$ by moving a frame around: effectively the algorithm for a person walking around on the surface of the sphere to determine the next point would be to turn left by $\theta_1$ then walk forward by $\theta_2$. This would always seem to converge to some tour of a small number of points, which perhaps should be obvious in retrospect. | |
| May 16, 2010 at 3:28 | comment | added | Henry Segerman | @Wadim: It's mostly curiosity, although I would be very interested in such a construction for artistic purposes. I've used the 2D version many times. | |
| May 16, 2010 at 2:58 | comment | added | Robby McKilliam | Is the sunflower spiral the densest packing in $\mathbb{R}^2$ constructed in this manner? That is, by continued scaling and rotation | |
| May 16, 2010 at 2:16 | comment | added | Wadim Zudilin | @Henry: Is that a curiosity question, or you have reasons to ask it? I wonder whether you have tried to construct 3D analogues yourself. Something interesting or nothing? | |
| May 16, 2010 at 1:53 | history | asked | Henry Segerman | CC BY-SA 2.5 |