Timeline for Does the Mandelbrot set have infinite VC dimension?
Current License: CC BY-SA 3.0
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| Jul 18, 2016 at 20:28 | comment | added | Aryeh Kontorovich | Good question. Since even a sinusoid, appropriately scaled and shifted, has infinite VC-dim, I would wager that so does the Mandelbrot set. I remain agnostic regarding the stronger claim. | |
| S Dec 29, 2015 at 14:19 | history | suggested | Adam | CC BY-SA 3.0 |
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| Dec 29, 2015 at 13:54 | review | Suggested edits | |||
| S Dec 29, 2015 at 14:19 | |||||
| Dec 21, 2015 at 7:02 | comment | added | Peter Schmidt-Nielsen | I made a little numerical progress on this. By writing a program that does blind brute-force search I found a set of 12 points that I could shatter, showing numerically that the VC dimension is at least 12. To get much beyond this I'll clearly need a less brute-force approach, though. | |
| Dec 18, 2015 at 9:39 | comment | added | André Henriques | Here's a rephrasing of your question 2 (essentially unpacking the definition). Let $A$ and $B$ be two disjoint finite subsets of $\mathbb C$. Does there exist a similarity $\theta:\mathbb C\to\mathbb C$ of the complex plane such that $\theta(A)$ is contained in the Mandelbrot set, and $\theta(B)$ is contained in the complement of the Mandelbrot set? | |
| Dec 18, 2015 at 9:28 | review | First posts | |||
| Dec 18, 2015 at 10:43 | |||||
| Dec 18, 2015 at 9:25 | history | asked | Peter Schmidt-Nielsen | CC BY-SA 3.0 |