Think of water flowing out of a nozzle: the pattern of the water spray depends entirely on the shape of the nozzle (straight pipe vs. a garden hose rose head), just as the shape of a wire determines the spatial pattern of its magnetic field.

Shape Shapes Field (SSF): Shape of conductor determines the Shape of the Field.

According to the Biot-Savart Law and Ampere's Circuital Law, the magnetic field $B$ at any point around a conductor is determined by the current $I$, the distance from the conductor, and crucially, the spatial distribution and shape of the conducting path. The shape of the conductor dictates the direction and superposition of the magnetic field vectors produced by each infinitesimal current element ($\text{Idl}$).