This is called troxler fading. Images in your eye disappear when they are held steady on the eye. You don't realize it but when you are looking at an object your eye is always making very small movements (called microsaccades) to destabilize your central vision. These microsaccades are not enough to destabilize your peripheral vision because your peripheral vision have very large receptive fields. This causes the purple dots to disappear. The green dot that is present when the purple dot disappears is due at an afters image effect that occurs due to opponent process theory of color vision. Basically what happens is red and green sensitive cones feed into the same neuron so they oppose each other (ie. one object cannot be both blue and green at the same time). When the purple is presented it bleaches out the red cones, so when it disappears the visual system interprets it as the opposite color being presented, in this case green. For more explanations on visual illusions check out /r/optometry (shameless plug).