Thanks for all your replies.
Isaac: the noise pattern is in the blue channel.
I've added the three channels to this page:
K20d ISO Noise
Lowell: the image is not a background. I took all the pictures yesterday. It's actually of the side of a workbench in my lab (I'm a Physics teacher). I chose it becuse the noise is easiest to see over a dark background.
Jack: it is present in light pictures too. I took similar pictures of my whiteboard and the purple glow is still there, but as it appears as a lightening of the blue channel, it was less noticable as the blue channel was already light.
I think I'll contact Pentax to see if it is a warranty issue. I've only had the camera for two weeks.
I should have said that all these pictures were shot in manual mode with the DNG setting and imported into Lightroom. There has been no editing other than ensuring the white balance was consistent for all the shots (taken under fluorescent lights with auto white balance) and resizing for web. No changes were made to the exposure in lightroom. The nose was clearly visible on the camera's screen which prompted me to take these test shots.
Thanks,
Mike