'square-patterned' originates from English, composed of the adjective 'square' and the past-participial adjective 'patterned' (from 'pattern').

'square' comes ultimately from Latin 'quadrātus' (from 'quattuor', meaning 'four'), passed into Old French (e.g. 'esquarre') and Middle English before becoming modern English 'square'; 'pattern' comes from Old French 'patron' (model), from Latin 'patronus', and 'patterned' is formed as the past-participle/adjectival form of 'pattern'. The compound 'square-patterned' is a modern English compound combining these elements.

Initially, 'square' primarily referred to the geometric shape 'a four-sided figure'; over time, in compounds like 'square-patterned' it came to be used in describing surface decoration or designs composed of squares.