To creep or spread gradually over something; to cover by slow creeping motion.
From 'be-' combined with 'creep' (from Old English creopan, Germanic root). The prefix intensifies the creeping action across a surface.
Ivy and vines 'becreep' buildings—this is exactly the word Victorian naturalists used when describing how fast-growing plants slowly took over walls and structures. Watching time-lapse of ivy growth, you understand why: it creeps so completely and thoroughly that 'becreeping' feels like the perfect word.
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