Leaf miner damage wouldn't be that thorough and uniform.

It looks viral to me. Anemones are susceptible to various viruses. I'd send samples to the plant pathology lab in Puyallup for a firm diagnosis but roguing out virus infected plants is pretty much SOP.

Thanks to you both for the replies. Since I reside in Oregon I can send samples to OSU plant clinic and meanwhile cull out the offending plants although admittingly I find the leaves rather interesting.

It could be an interesting sport. I like it.

I'd also get it checked out. I'll bet the plant geeks at OSU would love to see it.