Detailed experimental studies of the dynamics of self-trapped beams of white light (400-800 nm) in a photosensitive organosiloxane medium are presented. Self-trapped white light beams with similar spatial profiles formed in the organosiloxane at intensities ranging across an order of magnitude (2.7-22.0 W.cm(-2)). Beam-profiling measurements showed that these spatially and temporally incoherent wave packets propagate without diffracting (broadening) by initiating free-radical polymerization of methacrylate groups and corresponding refractive index changes in the organosiloxane medium. Analyses of their temporal evolution showed that the intensity-dependent behavior of self-trapped white light is similar to that of self-trapped laser light despite the extreme differences in their phase structure and chromaticity; the self-trapped incoherent beams even show the complementary oscillations of width and intensity that is characteristic of self-trapped coherent light. Furthermore, the dynamics of the self-trapped white light beams was found to be strongly correlated to the kinetics of free-radical polymerization and corresponding rates of refractive index changes in the organosiloxane. These studies provide accessible photochemical routes to self-trapped incoherent wave packets, which are extremely difficult to generate in conventional nonlinear optical media that owe their responses to higher-order dielectric susceptibility tensors. This could enable the experimental verification of theoretical models developed for the nonlinear propagation of white light and stimulate research into more complex self-trapping phenomena such as the interactions of self-trapped incoherent beams and spontaneous pattern formation due to modulation instability in a uniform incoherent optical field. These findings also carry potential for the development of self-induced waveguide, optical solder and interconnect technology for incoherent light emitted by incandescent sources or LEDs.