Timeline for Fractal-like structures arising from the action of a group on $\mathbb{Z}^2$
Current License: CC BY-SA 3.0
16 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 26, 2017 at 0:23 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Updated image links.
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| Jul 28, 2014 at 10:08 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Added a link to a video showing additional pictures of spheres under the action of G on Z^2.
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| Apr 15, 2014 at 18:16 | comment | added | vzn | this appears to be a case of what are known by some as "collatz like functions". eg sec 1.4 & others of new/recent paper Problems in number theory from busy beaver competition by Michel. basically these problems are difficult to study & lie at the boundary of decidable and undecidable & are an open/active area of research. | |
| Mar 17, 2014 at 14:32 | answer | added | Sebastien Palcoux | timeline score: 11 | |
| Mar 17, 2014 at 11:31 | comment | added | Sebastien Palcoux | What beautiful pictures! An animation showing successively all the spheres from radius 0 to radius 45 would be interesting too: one animation with a fixed scale, and one with a renormalized scale. Do you observe that the shape of the spheres (at renormalized scale) "converge" to a (unique) fractal shape (I hope my question is understandable) ? | |
| Mar 16, 2014 at 22:39 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Added a picture of the sphere of radius 45 about (0,0) under the action of G at a scale of about 1:100, as well as links to pictures of the spheres of radius 30 and 36.
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| Mar 14, 2014 at 18:45 | comment | added | Sebastien Palcoux | Besides the fractal structure, the spheres look like to an explosion, I had never seen such pattern in pure mathematics. I don't know if there is something to say mathematically about that, perhaps such group actions appear in a discrete modelling of physical explosions. | |
| Mar 12, 2014 at 21:34 | history | edited | Stefan Kohl♦ |
Added tags ds.dynamical-systems and fractals, following Sebastien Palcoux' suggestion.
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| Mar 12, 2014 at 12:51 | comment | added | Sebastien Palcoux | Why don't you put the tags ds.dynamical-systems and fractals ? Experts of these subjects could help you (there are others fractal-like phenomenons on discrete strutures, for example the Rauzy fractals). | |
| Mar 12, 2014 at 2:48 | comment | added | Noah Schweber | This is a wonderful question! | |
| Mar 11, 2014 at 20:50 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Added list of cardinalities of spheres of radii 0 .. 45.
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| Mar 11, 2014 at 20:36 | comment | added | Stefan Kohl♦ | @PerAlexandersson: see my comment below your answer. | |
| Mar 11, 2014 at 20:00 | comment | added | Per Alexandersson | Hm, what do you mean by the sphere here? You are looking at the forward orbit of (0,0) under all maps, are you not? | |
| Mar 11, 2014 at 19:26 | answer | added | Per Alexandersson | timeline score: 3 | |
| Mar 11, 2014 at 18:33 | history | asked | Stefan Kohl♦ | CC BY-SA 3.0 |