It happens that, in this case, there is additional information that can be used. By re-calculating with a "distance estimator" algorithm, points were identified that are very close to the edge of the set, so that unusually fine detail is aliased in from the rapidly changing escape times near the edge of the set. The colours derived from these calculated points have been identified as unusually unrepresentative of their pixels. The set changes more rapidly there, so a single point sample is less representative of the whole pixel. Those points were replaced, in the third image, by interpolating the points around them. This reduces the noisiness of the image but has the side effect of brightening the colours. So this image is not exactly the same that would be obtained with an even larger set of calculated points. To show what was discarded, the rejected points, blended into a grey background, are shown in the fourth image.