Here's some early footage of Robert Smith performing with Siouxsie and the Banshees, a post-punk band founded by Sex Pistols follower Siouxsie Sioux. Considering the stripped-down minimalism of punk rock itself, it's interesting to see how many different styles and musical directions evolved out of the early punk rock scene.
Siouxsie Sioux was one of a number of young punk rockers who frequently attended Sex Pistols shows and supported the band. Another member of that early group of Sex Pistols fans was a London Irish kid named Shane MacGowan. Siouxsie went on to form Siouxsie and the Banshees, and helped to create the gothic subculture in the process. One of her early bandmates, Robert Smith, had just as much of an influence on both the goth scene and post-punk music through his own band, the Cure.
Shane MacGown, on the other hand, took the raw energy and speed of punk rock and combined it with the folk music of his Irish homeland with his band the Pogues. This, in turn, led to later “Irish punk” outfits like the Dropkick Murphys and Flogging Molly.
Listening to the music of such diverse bands as the Cure, the Pogues and Siouxsie and the Banshees, it's almost difficult to believe all of this is somehow tied together- but it really is. It all had its origins in a few young people who saw the Sex Pistols perform and got excited about making music. It isn't so much the sound of punk rock that was influential, but the anarchic burst of creativity.