Biophysicists are modeling conformations of interphase chromosomes, often basing the strengths of interactions between segments distant on the genetic map on contact frequencies determined experimentally. Here, instead, we develop a fitting-free, minimal model: bivalent red and green transcription factors bind to cognate sites in runs of beads (chromatin) to form molecular bridges stabilizing loops. In the absence of additional explicit forces, molecular dynamic simulations reveal that bound factors spontaneously cluster -- red with red, green with green, but rarely red with green -- to give structures reminiscent of transcription factories. Binding of just two transcription factors (or proteins) to active and inactive regions of human chromosomes yields rosettes, topological domains, and contact maps much like those seen experimentally. This emergent bridging-induced attraction proves to be a robust, simple, and generic force able to organize interphase chromosomes at all scales.