I realised I had this basic question which I didn't really think about it till now.
I'm wondering when we change the chord, are we supposed to "reset" the strumming pattern?
Let's say we are playing this strumming pattern: D D DU D
So let's say the chord change falls on the 3rd Down. Are we supposed to go back to playing "D D DU D" when we change the chord or do we just continue strumming at where we left off- "DU D" i.e.?
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You keep going with the pattern in that case. So you'd strum D D on the first chord and DU D on the second, like you said.
Professional lurker since 2009.
you can do what sounds good i recently realized this too and it is tricky to get the hang of but i have found it opened a lot of new doors to chord progressions and strum patterns.
Man these things doesn't matter do what helps you out, these kind of details don't matter when you reach a certain level. You have to do what works for you, everybody has it's own style of strumming chords, while certain pattern are usually the most used, this doesn't mean that you have to do it.

If you have another idea go for it,music is about sound not about how you play it technically
The best thing to do is to maintain your strumming pattern - it helps you keep consistent and keep time, otherwise you'll end up doing upstrokes on the 1st beat (which is fine, I suppose, but not desirable). Best thing to do is to try to make sure you down pick on the odd number or the lowest common denominator (OK this sound weird: what I mean is this):

Say you're playing in 4/4 timing and have a 16th followed by 3 8ths, then a 16th, then 4 8ths. The pattern would be D U U U D D D D D.