To scatter or spray liquid or sticky material in irregular directions and patterns.
From Middle Dutch 'splateren' or related Germanic words imitating the sound of splatting. The word is onomatopoetic—it imitates the actual sound something makes when it splatters.
Splatter painting, made famous by Jackson Pollock, is actually based on physics—the angle and speed you throw paint determines where it lands, and artists like Pollock used this science to create seemingly random but mathematically patterned artwork.
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