Timeline for "Fractally self-similar" numbers
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2015 at 8:33 | vote | accept | მამუკა ჯიბლაძე | ||
| Nov 30, 2015 at 18:57 | comment | added | მამუკა ჯიბლაძე | Yes I see now - there is no real difference between "outside" and "inside" given transformations that interchange them. One more question though, about the penultimate paragraph - I don't quite see why in case of growing denominator ratios the pictures will converge to a zoomed-out picture: in case of quadratic irrationality there was that unique conjugate and iterates of the inverse of $f$ accumulated to it. But if now $\phi$ is not quadratic anymore, not even algebraic, why will turning the process backwards yield convergence to anything? | |
| Nov 30, 2015 at 18:13 | comment | added | Adam P. Goucher | You can reconstruct all the circles. Specifically, given three externally tangent discs in $\mathbb{C} \cup \{ \infty \}$ (two of which are the interiors of those two circles; the other is the lower half-plane), you can uniquely construct an Apollonian disc packing. The Ford circles are precisely the discs in the Apollonian gasket which are tangent to the real line. | |
| Nov 30, 2015 at 18:07 | comment | added | მამუკა ჯიბლაძე | Still trying to digest your answer. The key point seems to be much the same as with my previous question - that two circles determine the rest. Except more precisely they determine the portion of the tesselation confined between them, I don't quite see how to reconstruct anything outside. | |
| Nov 30, 2015 at 15:50 | history | answered | Adam P. Goucher | CC BY-SA 3.0 |