Hasta La Motion!

I’m trying to create a time mapping effect in which each pixel will be taken from the same position of the source sequence but from a moment in time defined by a b/w matte called time map. So for example if I have a sequence going thru the time mapper and using a b/w top down gradient (white up and black down) as time map and I gain that time map from 0 to 1 the effect will be that the top of the frame will play earlier time than the the bottom of the frame which will play later time. I don’t know if this is making sense to you but if you’re familiar with fusion it has similar tool. There’s also the custom tool in fusion where you can define the value of each pixel using a formula so if there’s something similar in nuke that’s another way to do it. Basically if you define the start of the range and end of the range of the time you need to map:
RGBresult(t)=RGBsource(ValueOfTimeMap(t)*(EndOfRan ge-StartOfRange)+StartOfRange)