cartoonist:
To me it looks like you need to do a clear screen, fill the display memory with all zero's or one's, before you write new data to the display, otherwise you will write over the old data. The noise you see after bootup is your display-memory that has undefined states and that looks just like noise.
I think this wouldn't solve the problem because I've tried differend examples with all the same problem. Fill the display with zero's will maybe solve de noise problem on startup but not problem that all the images of the demo (circles, waves etc) are stacked on top of each other.