Timeline for Complexity of the Mandelbrot set on rationals
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2017 at 19:00 | comment | added | Adam | Maybe : Computing a “long” iteration : arxiv.org/abs/math/0505036 | |
| Nov 15, 2017 at 16:43 | comment | added | Phylliida | Again all this stuff on decidability is interesting but completely unrelated to this question. I’ll stop saying this now but generally discussions in comments shouldn’t go too long and you guys are flooding it | |
| Nov 15, 2017 at 16:38 | comment | added | Adam Epstein | @AndrejBauer Sorry, not known! I can't supply a written reference that this is not known to b decidable. But, for example, Milnor has posed this with reference to particular rational numbers. | |
| Nov 15, 2017 at 14:37 | comment | added | Phylliida | @AdamEpstein that doesn’t really matter though in this case because I only care if it escapes after k iterations. | |
| Nov 15, 2017 at 13:42 | comment | added | Andrej Bauer | @AdamEpstein did you mean to say not known and do you know a reference? | |
| Nov 15, 2017 at 13:00 | comment | added | Adam Epstein | @AndrejBauer It appears to be known whether the following even more elementary problem is algorithmically decidable; Given $c\in\Bbb{Q}$, determine whether or not $c$ lies in the interior of the Mandelbrot set. It should be noted that the latter condition is equivalent (via highly non-elementary considerations) to the more elementary condition that $z\mapsto z^2+c$ has an attracting cycle. | |
| Nov 15, 2017 at 5:35 | answer | added | Phylliida | timeline score: 4 | |
| Oct 21, 2017 at 20:44 | comment | added | Phylliida | @AndrásSalamon that’s an interesting question and certainly related but how does it help here? | |
| Oct 21, 2017 at 8:40 | comment | added | András Salamon | See related question (and its answers) math.stackexchange.com/questions/1035215/… | |
| Oct 13, 2017 at 6:54 | comment | added | Andrej Bauer | @FedericoPoloni: Hertling, P. (2005), Is the Mandelbrot set computable?. Mathematical Logic Quarterly, 51: 5–18. doi:10.1002/malq.200310124 | |
| Oct 12, 2017 at 21:22 | comment | added | Federico Poloni | @AndrejBauer Do you have a reference for this? | |
| Oct 12, 2017 at 21:06 | history | edited | Phylliida | CC BY-SA 3.0 |
Computations isn't correct wording this is
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| Oct 12, 2017 at 14:50 | history | edited | user44143 | CC BY-SA 3.0 |
added 35 characters in body
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| Oct 12, 2017 at 14:29 | answer | added | Joe Silverman | timeline score: 5 | |
| Oct 12, 2017 at 9:22 | comment | added | Andrej Bauer | I don't have an answer, but the following might help. It is not known whether the following problem is algorithmically decidable: Given $p, q \in \mathbb{Q}$ and $k \in \mathbb{N}$, determine whether the open circle with center at $p + q i $ and radius $2^{-k}$ intersects the Mandelbrot set. | |
| Oct 12, 2017 at 9:19 | comment | added | Andrej Bauer | Actually, my point is that something like 65535 doesn't do any harm, so long as you avoid large "black" blobs. In most pictures that people make there's hardly any points of the Mandelbrot set, they're all just the exterior (but very close to the set), and of those only very few, if any, require more that several thousand iterations to escape. So there's no discernible change in speed if you crank ut up to 65535. (Anyhow, this is beside the point.) | |
| Oct 12, 2017 at 7:06 | comment | added | Phylliida | @AndrejBauer lol true, though that is with floating points (which are somewhat accurate even zoomed in a lot without needing too much precision via using perturbation theory) but if you are forced to use rationals and not accept rounding error is there an easy way to do even like 100 iterations? | |
| Oct 12, 2017 at 7:01 | comment | added | Andrej Bauer | Pickiing 50 is so 1980's. These days we pick 65535. | |
| Oct 12, 2017 at 6:20 | history | asked | Phylliida | CC BY-SA 3.0 |