Confusion over Google Analytics (GA) Absolute Unique Visitors data - google-analytics

GA Unique Visitors data isn't making sense to me. From the GA FAQ we get the following definition for 'Visits vs. Visitors'
"The initial session by a user during any given date range is considered to be an additional visit and an additional visitor. Any future sessions from the same user during the selected time period are counted as additional visits, but not as additional visitors. "
The part that I can't resolve with the GA graph is "Any future sessions from the same user during the selected time period are counted as additional visits, but not as additional visitors". For the graph below covering a 30-day period, I would understand the GA definition to mean that the data represents uniqueness across all 30 days, right? But if you look at the screen shot below, you see a regular pattern for each week over the 30-day period the report covers. From that, it seems the numbers we are seeing associated with each of the days of the graph (e.g. 3.92% (4142) for Tuesday, September 8) is a count of unique visitors just in the context of that one day - i.e. without correlating their uniqueness to the rest of the days in the 30-day period. If the graph actually showed uniqueness across the 30-day period, I would expect the daily numbers to start high in the early days of the period and decrease over the 30-day period as the number of already-seen visitors (i.e. returning visitors) increases, no?
What am I missing here?
UPDATE
Helpful clue from Jonathan S. below got me on the right track.
I think I understand now what the daily bar graph values mean, but it's a little counter-intuitive and I'd bet not what some others might be assuming as well. The reports states "39,822 Absolute Unique Visitors" at the top, which means just that: over the 30-day period we saw this many uniques. Fair enough. The confusing part is that the daily (or weekly) bar values in the graph below are not mutually exclusive uniques as I had assumed, but are values relative only to the 39,822 total - i.e. there is overlap between the unique visitor counts across any group of days. This means the sum of the daily % values > 100% and the sum of the daily count values > 39,822. The algorithm is: when you visit for the first time in the 30-day period, call that "today", you add 1 to the total (39,822) and 1 to the "today" bar value. When you show up again "tomorrow", you are NOT counted again in the total, but ARE counted as 1 in the "tomorrow" bar value.
alt text http://img.skitch.com/20090922-djti81ejj5gqn575ibf8cj1e8x.jpg

I believe it's just an issue of grouping. The top right of the graph has 3 icons to group by day, week, or month. It's currently grouping by day. So if I visit your site today and come back tomorrow, I'll be counted once for each day.
I tried looking at the month view for one of my sites but it didn't give me much meaningful data. I believe the above should answer your original confusion though.

Is it possible that you're searching for something what isn't existing anymore? Unique Visitors/Visits is old terminology. Check: https://www.seroundtable.com/google-analytics-sessions-users-18424.html
Then check how sessions and users are defined:
Sessions ("ex-visits", it's very detailed): https://support.google.com/analytics/answer/2731565?hl=en&ref_topic=1012046
Users in Google Analytics reporting are defined as "Users who have initiated at least one session during the date range". So IMHO it's not about 30 days, it's about the SELECTED date range.
I hope this helps.

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