Free-space volumetric displays, or displays that create luminous image points in space, are the technology that most closely resembles the three-dimensional displays of popular fiction. Such displays are capable of producing images in 'thin air' that are visible from almost any direction and are not subject to clipping. Clipping restricts the utility of all three-dimensional displays that modulate light at a two-dimensional surface with an edge boundary; these include holographic displays, nanophotonic arrays, plasmonic displays, lenticular or lenslet displays and all technologies in which the light scattering surface and the image point are physically separate. Here we present a free-space volumetric display based on photophoretic optical trapping that produces full-colour graphics in free space with ten-micrometre image points using persistence of vision. This display works by first isolating a cellulose particle in a photophoretic trap created by spherical and astigmatic aberrations. The trap and particle are then scanned through a display volume while being illuminated with red, green and blue light. The result is a three-dimensional image in free space with a large colour gamut, fine detail and low apparent speckle. This platform, named the Optical Trap Display, is capable of producing image geometries that are currently unobtainable with holographic and light-field technologies, such as long-throw projections, tall sandtables and 'wrap-around' displays.