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If you have a cartoony style character you can get away with doing polygon hair either has hair cards or larger objects and use either cloth physics or soft body on them which should be less intense than particles but might still be a bit much for your laptop ^_^; (and also I can't help with those as I've never managed to get good results which is one of the reasons why I ended up doing particle hair XD)

I have a laptop I acquired recently to be able to keep working while travelling and it's so violently lower spec'd than my current rig I'm scared about how things are going to go on it, so can totally sympathise with the waiting for an upgrade XD

yeah it's interesting seeing what pushes the limits. I think when I do actual characters I'll use the block style hair, I don't intend to ever actually animate any characters on here so hopefully I can manage. I'm pretty sure it would explode if I tried that.