Distorting a drawing with noise

How do I draw a noise following a drawn shape?
When I draw a circle, I want it to be distorted by a noise.
Like in Island Generator, but I don’t want to use the Marching Square extension, which is limited to the camera field.
I’ve tried many times to butcher Island Generator, but I just can’t do it.

What’s the current result?
I draw shapes but I can’t apply noise to them.

Related screenshots

use the noise effect on base layer, only affect paintcursor

Hello, I didn’t understand your answer. My problem is that I can’t draw the noise.

hmm. let me think…
Put a grain background into the scene, then put a white background on top and make it so that when you draw, it erases the white, creating the illusion of a grain pen line.