Timeline for Set operations over iterated function systems
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2019 at 18:49 | comment | added | Dev Sinha | The underlying fact which makes this not so surprising is that totally disconnected spaces are dense in the space of all metric spaces. (Pointillism at work!) | |
| Nov 29, 2019 at 18:48 | comment | added | Dev Sinha | I recall this being proved in Barnsley's book. Examples of what you are looking for are plentiful. Consider the IFS on the real line with two affine maps which shrink to 0 and 1 with stretch factor s, so $s=1/3$ gives the Cantor set. As $s$ passes from $s < 1/2$ to $s = 1/2$ the attractor goes from being totally disconnected to connected. | |
| Nov 29, 2019 at 13:55 | comment | added | Zorngo | Do you know of a good reference for your second statment? I'm curious as to what happens if you go from a totally disconnected attractor to a connected attractor by continuously varying the IFS. | |
| Oct 30, 2019 at 12:35 | history | answered | Dev Sinha | CC BY-SA 4.0 |