How to build up luminance values that pass through a frame

Hello,

I am trying to create an effect where a layer remembers all the luminance values that pass through it.

To describe the effect imagine a white dot was to pass through a black frame from left to right. As it passes through the black frame it would create a white line since the effect would remember and retain all the luminance values as the white dot passes through it. If a continual stream of white dots where to pass through the entire frame eventually the frame would become filled with white as at some point white dots would have occupied all the space in the frame.

I think I might be able to achieve this with one of the time echo effects but would love to hear if anyone else has any experience with this type of effect.

Thanks a lot for any help here.

Spencer