I have an image prepared with transparency, like this:

With two UIviews, I configure the background colors as so:
self.view.backgroundColor = [UIColor groupTableViewBackgroundColor];
self.dashedView.backgroundColor = [UIColor colorWithPatternImage:[UIImage imageNamed:@"red_square.png"]];
I expect the red square to be repeated over the UIView with transparency preserved, but it’s been filled by a solid color like this:

I don’t understand why. Is there a simple way to draw a tiled image with transparency? Or do I need to look at drawing Core Graphics patterns?
Pattern images should be keeping the transparency just fine.
Try
[self.dashedView setOpaque:NO]