Timeline for Optimization of points on a plane
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2015 at 20:48 | comment | added | Halbort | I reached an equilibrium that involved a 7-gon. I think all regular polygons with some centroid points are equillibirum. The pentagon seems to be the most stable though. | |
| Dec 9, 2015 at 3:13 | vote | accept | Halbort | ||
| Dec 8, 2015 at 23:40 | comment | added | Per Alexandersson | @Halbort: Oh, there was a brace missing at some point - it should work now. I use Mathematica 9, by the way. | |
| Dec 8, 2015 at 23:39 | history | edited | Per Alexandersson | CC BY-SA 3.0 |
added 1 character in body
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| Dec 8, 2015 at 22:53 | comment | added | Halbort | I keep getting {{k,Ceiling[Length[newLists$109483]/2],Length[newLists$109483]};\ newLists$109483=SortBy[newLists$109483,Fitness];gg=ListPlot[newLists$\ 109483[[1]],Axes->False,PlotStyle->PointSize[0.02`]]} does not have \ appropriate bounds. >> as an error. | |
| Dec 8, 2015 at 22:41 | comment | added | Halbort | I copy pasted it directly. I cannot see anything happening. Could you help me? | |
| Dec 8, 2015 at 22:38 | comment | added | Halbort | Where does the image get stored? | |
| Dec 8, 2015 at 21:29 | comment | added | Per Alexandersson | @GerhardPaseman: Yeah, you are right, seems like 6-gons, 5-gons and 4-gons are stable, but maybe not higher... | |
| Dec 8, 2015 at 21:28 | comment | added | Per Alexandersson | @Halbort: Open a notebook, paste the code, and run. It dynamically updates a picture with the best configuration, and does 1800 generations. | |
| Dec 8, 2015 at 20:05 | comment | added | Halbort | How do I run this mathematica code on my machine? | |
| Dec 8, 2015 at 20:00 | comment | added | Gerhard Paseman | You may be right, but then I think you would have seen that in your simulation. I suspect regular n-gons are minima only for n up to at most 6, because of the combinatorial explosion of diagonals. Gerhard "Leaves The Numerics To Others" Paseman, 2015.12.08 | |
| Dec 8, 2015 at 19:48 | comment | added | Per Alexandersson | @GerhardPaseman: Yes, but I think you will find that a regular n-gon, with the remaining dots in the center is a local minima... Perhaps one can argue that the ONLY local minima are of this form, and then it is easy to find which of these is global. | |
| Dec 8, 2015 at 19:46 | comment | added | Gerhard Paseman | It should be not too hard to show minimality by abstractly pushing dots around. Things inside the convex hull should gravitate toward a centroid, and points not too far outside the convex hull of the remaining points should be absorbable when there are at least 4 remaining points. Gerhard "Hand Waving Gives Some Elevation" Paseman, 2015.12.08 | |
| Dec 8, 2015 at 18:40 | vote | accept | Halbort | ||
| Dec 9, 2015 at 0:44 | |||||
| Dec 8, 2015 at 18:40 | comment | added | Halbort | I just realized that I messed up. | |
| Dec 8, 2015 at 18:32 | comment | added | Per Alexandersson | @Halbort: I get it to be $16/\sqrt{3}$... | |
| Dec 8, 2015 at 18:20 | comment | added | Halbort | For $n = 4$, if you make an equilateral triangle with one point in the center I think you get $4\sqrt{3}$ | |
| Dec 8, 2015 at 18:05 | history | answered | Per Alexandersson | CC BY-SA 3.0 |