Normally, purple in the poems of Dickinson often refer to the royal purple colour worn by Christ in heaven, therefore symbolising his majesty, imperial nature and power. However, in this poem, which is clearly a poem describing the beauty of a sunset and a sunrise, it appears that the colour purple does not have this Christian significance, and rather just merely is an attempt to describe the beautiful chaos of colours that are part of a sunset. Consider how it is used in this poem:
There seemed a purple stile.
Which little yellow boys and girls
Were climbing all the while
We can see that a metaphor is used to describe the sunset as the speaker imagines that little yellow boys and girls are climbing up the "purple stile" as she watched the sun slowly set and the riotous colours that occur as a result. Purple therefore seems, in this poem at least, not to have any symbolism in particular apart from the attempt to describe the beauty of the sunset on paper.