frozen screensaver - psychedelic colouring - image attached.

I think dialabrain is on the right track however we can also look to see if there is anything obvious on your system that may be causing a problem. If you would like to check that please do the following:

Please navigate to the Mac App Store and download the free version of EtreCheck OR please click www.EtreCheck.com where you will find the app. Once you downloaded the free app and created the report please post it as your reply to this message. In order to post it, please use the following link for more detailed instructions on how to correctly include the results: 

https://discussions.apple.com/docs/DOC-250000211

We can then look for obvious issues that may be causing your problem.

There are 2 issues, however I do not believe either is connected to your current problem. First is, your computer is starved for RAM and you should upgrade to 16GB or more of RAM. 8GB is considered the bare minimum to run current versions of Mac OS. If you decide to take the step to upgrade please only use RAM from either Crucial.com or Macsales.com . The reason for recommending these 2 vendors is iMacs are very sensitive to using quality RAM and both vendors have long histories of providing high quality products, reasonable prices and great service.

Next, I don't see any evidence the computer is being backed up. This is very dangerous and is an almost certain guarantee of lost date including financial information, irreplaceable music, photos, and other precious data. At a bare minimum you shoudl be using Time Machine as explained in https://support.apple.com/en-us/HT201250 . You will need an external HD (I recommend Macsales.com again and use their Mercury Elite Pro series of EHDs.

That one is abstract shapes - and I should have said Desktop for that one, as that freeze was on lock screen - it freezes on different screensavers. I experimented by running the random screen saver and it would freeze on different ones.

Abstract Shapes is not a default Apple screen saver so I assume it's something you downloaded. The problem might be some screen savers are no longer compatible.

If you want to get Crucial RAM, please only purchase it from Crucial.com . They make the process easy by using a configuration tool. I don't know the reseller you are referring to (I'm in the USA) and have learned from experience not all Crucial RAM is alike from resellers. This is why I recommend buying from Crucial.com direct.

As for the configuration type either 4x8GB or 2x16GB kits would be okay.

Which screen saver is that? do all the screen savers do that?

Out of curiosity, do you have any antivirus apps or cleaning apps installed on the computer?

Thanks and yes, you are correct Mac OS does not need any third party maintenance apps. I was checking to see if using an AV or cleaning app may be the cause. It clearly is not.