Apps can't change their own app icon

Some apps would be more useful and/or delightful if they could change the appearance of their own app icon, even when the app is not running.

For a couple of apps this is important:
- It is misleading for the Calendar app icon to show a date that isn't the current date (bug 1362962).
- It is also misleading for the Clock app icon to show a time that isn't the current time (bug 1362964).

For other apps it would be just nice to have:
- A Weather app would be more useful if its icon showed the current weather (against a sky reflecting the time of day) without you having to open it.
- The Gallery icon could include thumbnails of your most recent 3~4 photos.
- A Reminders icon could miniaturize the start of the frontmost note (similar to Nautilus's icons for text files), which might occasionally save you from opening the app.

This might be achieved by having an API for any app to update its own icon on a timer -- for example the Weather app might ask for the opportunity to update its icon every 30 minutes.

Or it might be achieved by hard-coding Clock and Calendar icon updating inside Unity. (This would probably be necessary for a Clock icon to have an updating second hand.)

Or there might be a combination of both approaches.