The DatePattern string needs to be something that the SimpleDateFormatter will accept.
Unfortunately this means that, out of the box, this doesn't include being able to set the boundary to be a week number. There are ways of getting this value in C#, but it's not obvious that we can extend the SimpleDateFormatter or provide a different implementation of IDateFormatter and use that instead (or even in a custom RollingFileAppender).
So how might we get a Log4Net RollingFileAppender to roll weekly?