For pt.I see ibid., p.Z004024-7. For pt.II see ibid., p.Z004558-61. This paper examines the rendering of luminous spots ("phosphenes") in the visual field, and their stochastic positioning as a means of anti-aliasing the resulting spotty image ("phosphene image"). We derive an equation concerning the correlations of pairs of phosphenes comprising the phosphene image, and show the relationship to the statistics governing the stochastic positioning. We present some examples where stochastic rendering assists the veridical perception of textures, and argue for its superiority as cf. ordered rendering. Our preliminary results suggest that it may be perceptually effective to manufacture disordered arrays of stimulating electrodes for intraocular implantation.