Scatter probably shares its origin with shatter — both carry the idea of breaking something into fragments that fly apart. The word may trace to a Proto-Germanic root meaning 'to spring'.
To throw or distribute in various random directions; to move apart quickly in different directions.
From Middle English scateren, probably from a dialectal variant of shateren meaning 'to shatter, to break apart'. The word may derive from an unattested Old English *sceaterian or from Old Norse influence. It is related to shatter, which shares the idea of breaking into fragments and sending pieces in all directions. The semantic link is clear: to scatter is to distribute things as if they had been shattered. Some scholars
Scatter and shatter are likely siblings from the same Germanic root. The connection makes intuitive sense — shatter a glass and you scatter the fragments. A scatterbrain, first recorded in the 18th century, is someone whose thoughts have been shattered into pieces and flung in every direction.