Gaussian Blur for a Dot

Hello all! I'm trying to do something very simple, but for whatever reason, I'm stumped. All I need to do is blur a dot on a screen. The size and color of the dot must be dynamic, as we'll be using different dots of different sizes and different colors. Also, the background of the dot must blend into the background of a figure. For example, let's say that I need a black dot on a white background. The white outline of the image must blend in perfectly with the white background of the rest of the screen. In other words, there can't be a noticeable border between where the image ends and the background begins.

Thanks so much!!!

Bill