When Ken Perlin described doing this, he called it "sum 1/f(noise)", referring to it as a fractal progression.http://www.noisemachine.com/talk1/21.html
It took me a while to figure this out. (It took a while for much about using noise to "click" for me!) By his formula, you would add half as much for each iteration.
Or another way to think about it: make the result a weighted sum, with the weights in a series that keeps dropping by a factor of 2.
1+2+4+8 = 15, so 8/15 * the lowest octave + 4/15 * the second octave + 2/15 * the third octave + 1/15 * the top octave (if you had four octaves).
By making it a proper weighting, you can ensure keeping the sum of the additions within the bounds [-1, 1].
In the visualizer app, the weighting occurs in the "mixer" (bank of sliders, lower left). In the "terrain" example, you'll see the values in the mixer dropping by 2's: 64, 32, 16, 8, etc. If you play around with the levels, you will find out that if the octaves are all given the same value, then the activity of the data at the top octaves will overpower the rest of the graphic.
Being a musician, I was bugged by the use of the term "octave." Part of the reason I built the dang visualizer was because I couldn't believe that the doubling relationships were all that magical in the visual realm, as they are in sound. And in truth, you don't
have to follow them strictly. But this fractal formula does seem to come up a lot, does have a basic niceness to it.