It doesn't seem to cascade:

Mediterranean creeping thyme - https://www.shootgardening.co.uk/plant/thymus-longicaulis

T. longicaulis is a mat-forming, evergreen perennial with small, linear to narrowly lance-shaped, aromatic, dark green leaves and clusters of tiny, bright pink flowers in summer.

Mediterranean Creeping Thyme is one of the most attractive varieties and best ground covers available.

https://www.brittanyperennials.uk/perennials-for-dry-poor-so...

Rapidly forms wide spreading mats of thin wiry stems, with mildly scented green leaves forming total ground cover. Completely covered in early summer with clustered heads of rosy-mauve flowers, much admired and ideal where something quick to cover the soil is needed.

http://www.bethchatto.co.uk/s-z/thymus/thymus-longicaulis.ht...

http://perennialle.com.au/thymus-longicaulis-mediterranean-c...

I think you have to include the "Mediterranean" because there is also Thymus serpyllum - https://en.wikipedia.org/wiki/Thymus_serpyllum


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Note added at 15 hrs (2017-11-09 10:37:02 GMT)
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Oh, I see, no I wouldn't put "creeping" there either, but probably something like "fresh thyme", "wild thyme" or something. I mean, it doesn't even say how much, and most thymes taste vaguely similar.