Revealing Fractal Noise effect from left to right

I would set up your fractal noise layer with the kind of animation you want and then set it on top of a shape layer with a gradient fill. Animate the start and end points of the gradient to get your wipe, set the blend mode for the fractal noise layer to overlay and end up with something like this:

This comp just needs to be slightly larger than your text layer. When you have the white to black comp animated add it to your main comp and use it as a luma track matte for your text layer. You'll end up with something like this:

This is only one of a couple dozen ways you could recreate the effect. Here's a project file for you to play with:

Dropbox - Fractal Noise Text Wipe.aep

(note: your browser may add a .txt extension to the AEP file when you download it, just remove it and you should be able to open the project and see what I have done)

You can add an additional effect to get what you are looking for. Use a Linear Wipe effect after the fractal Noise and use the result as aa luma matte for your text layer. You can find the Linear Wipe effect under the Transition category.