Substitute for grass - Zone 3a

Hey all!
I really enjoy reading the posts in here... Lots of useful and fun information... I noticed the posts about a lawn full of violets and can image that it looks really nice in bloom, but I guess with the grass able to grow tall that you couldn't really keep it natural.
I was just wondering, here in Calgary, Alberta... What would be a good substitute for a grass lawn? I'd still want something green. It would be great if it spread out instead of getting tall to avoid the need for mowing. Of course it would need to withstand some foot traffic. It it would flower it would even be nicer.
I doubt anything like this really exists as it would probably be pretty popular, but it can't hurt to ask, can it?
: )
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Looks very interesting.
THANKS!

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