Take a look at the figure above (taken from Mauriès 2003). What you're looking at is the intimate business of a male millipede, in this case a Bosnian millipede called Fagina silvatica. And if you ever had the pleasure of finding yourself working on millipede taxonomy, you'd be looking at a lot of these.
Fagina silvatica belongs to a superfamily of millipedes called the Neoatractosomatoidea, which is in turn part of the order Chordeumatida in the clade Helminthomorpha. Helminthomorph millipedes (as indicated by their name, which means 'worm-like') all cleave pretty closely to the classic image of their kind, with an elongate body bearing large numbers of relatively short legs. Chordeumatida are characterised by having silk-spinning glands on the telson, the very end segment of the body, and three pairs of strong bristles on the top of each body segment. Male chordeumatidans also have the eighth and ninth pairs of legs modified into the gonopods, the copulatory structures. Because millipedes are generally not extravagant animals in overall appearance, it is the gonopods that have become the primary structures for identifying them, and many millipede species cannot be reliably distinguished without examining them. In the Neoatractosomatoidea, the eighth pair of legs forms the gonopods proper that deliver the male's sperm to the female's vulvae, while the ninth pair form protective structures called paragonopods. The gonopods proper are divided into two branches that fold around each other, usually to guide a whip-like flagellum or other extended structure passing between them (one genus, Guizhousoma, lacks the flagellum—Mauriès 2005). One neoatractosomatoid genus, Osellasoma, also has the seventh pair of legs modified into protective structures (Mauriès 2003). Neoatractosomatoids have 28 or 30 body segments. Some neoatractosomatoids have the sides of the body extended into flattened processes called paraterga; others have the body more or less cylindrical. And no, I haven't been able to find a single photograph or illustration showing a neoatractosomatoid in its entirety. You'll have to content yourself with looking at their genitals (Wikipedia has photos of other Chordeumatida).
As defined by Mauriès (2003, 2005), the Neoatractosomatoidea only includes about 25 known species, mostly found in southern Europe. A single species, the aforementioned Guizhousoma latellai, is known from caves in China. Mauriès (2003) separated three families previously placed in the Neoatractosomatoidea into a separate superfamily Mastigophorophylloidea; if the mastigophorophylloids are included with the neoatractosomatoids, then the group includes further species found in northern Asia. Mauriès separated the two superfamilies on the basis that mastigophorophylloids possessed a flagellum on both the gonopods and the paragonopods, instead of only on the gonopods. The subsequent discovery of the entirely flagellum-less Guizhousoma could raise questions about the significance of this character, and the flagellum appears much reduced if not entirely absent on the paragonopods of at least one putative mastigophorophylloid, Kirkayakus pallidus, as illustrated by Mikhaljova (2004)*. However, I have to admit to having absolutely zero experience with interpreting millipede gonopods, so I am hardly one to be voicing an opinion.
*Mikhaljova (2004) illustrates this species under the name of Altajella pallida, but it has since been renamed by Özdikmen (2008) (yes, that Özdikmen) due to the original genus being preoccupied).
Mauriès, J.-P. 2003. Schizmohetera olympica sp.n. from Greece, with a reclassification of the superfamily Neoatractosomatoidea (Diplopoda: Chordeumatida). Arthropoda Selecta 12 (1): 9-16.
Mauriès, J.-P. 2005. Guizhousoma latellai gen.n., sp.n., de Chine continentale, type d'une nouvelle famille de la superfamille des Neoatractosomatoidea (Diplopoda: Chordeumatida). Arthropoda Selecta 14 (1): 11-17.
Mikhaljova, E. V. 2004. The Millipedes (Diplopoda) of the Asian Part of Russia. Pensoft: Sofia.
Özdikmen, H. 2008. New family and genus names, Kirkayakidae nom. nov. and Kirkayakus nom. nov., for the millipedes (Diplopoda: Chordeumatida). Munis Entomology & Zoology 3 (1): 342-344.