Aaaarrrrggghhhh....masks

Does anyone know if it’s possible to have several masks (over 20) on one image without repeating the image 20 times?

There is a lot of lines in the image and I want to make it appear as if the image is growing as the lines does, kind of like vines growing to create the image. Fastest I thought would be to mask the image and then reveal it a line at a time. Masks are the best way to do it…I think.

Any ideas/tips/hints…anything is appreciated cause I’m pulling out my hair here?