A double word that conveys the idea of drawing aimlessly is "doodle." It refers to making spontaneous or unconscious drawings, often while the mind is preoccupied with other thoughts. Doodling can serve as a creative outlet or a way to pass the time without a specific purpose.
The root word of "aimlessly" is "aim".
I aimlessly wandered the streets.
There are several words that mean 'to walk aimlessly', including:wandermeanderroam
I think it's Doodle, but you may have to check elsewhere
doodling
Aimlessly wandering through the desert sands, with the sun beating down, almost cost the explorer his life.
ramble
err
Aimlessly.
The word you are looking for is "doodle." Doodling refers to the act of drawing aimlessly or absentmindedly, often done while one is preoccupied with other thoughts or tasks. It is a common form of spontaneous and unconscious artistic expression.
Aimlessly is an adverb.
doodle