Born and raised in Harlem, ASAP Rocky — the ASAP standing for Accumulate Status and Power — took the rap world by storm with a catchy and melodic rap style that’s drawn immediate comparisons to acts such as Kool Moe Dee, Mase and Cam’ron. By not limiting his musical inspirations, however, Rocky creates much diversity in his music, which draws from the Red Hot Chili Peppers, Cee-Lo Green and MGMT, among many others. Because of his diversity and his rounds on the local battle-rap circle, his 2011 album, “LiveLoveA$AP,” created so much buzz that its single, “Purple Swag,” was receiving high-profile radio play even before it was officially released. ASAP Rocky performs at the National on Thursday, Feb. 9, at 8 p.m. $15-$18. 612-1900.