In microscopy, single fluorescence point sources can be localized with a precision several times greater than the resolution limit of the microscope. We show that the intermittent fluorescence or 'blinking' of quantum dots can analyzed by an Independent Component Analysis so as to identify the light emitted by each individual nanoparticle, localize it precisely, and thereby resolve groups of closely spaced (< lambda / 30) quantum dots. Both simulated and experimental data demonstrate that this technique is superior to localization based on Maximum Likelihood Estimation of the sum image under the assumption of point emitters. This technique has general application to any emitter with non-Gaussian temporal intensity distribution, including triplet state blinking. When applied to the labeling of structures, a high resolution "image" consisting of individually localized points may be reconstructed leading to the term "Pointillism".