Recently Deroin, Tholozan and Toulisse found connected components of relative character varieties of surface group representations in a Hermitian Lie grop G with remarkable properties. For example, although the Lie groups are noncompact, these components are compact. In this way they behave more like relative character varieties for compact Lie groups. (A relative character variety comprises equivalence classes of homomorphisms of the fundamental group of a surface S, where the holonomy around each boundary component of S is constrained to a fixed conjugacy class in G.) The first examples were found by Robert Benedetto and myself in an REU in the summer of 1992, and published in Experimental Mathematics in 1999. Here S is the 4-holed sphere and G = SL(2,R). Although computer visualization played an important role in the discovery of these unexpected compact components, computation was invisible in the final proof, and its subsequent extensions.