> image "noise" or "grain" that is introduced into a picture as you increase the ISO

Not this absolute shit again. This is not how photography works or how physics actually work. Image noise does NOT come from high ISO, it comes from low exposure (not enough light hitting the sensor). ISO is just a multiplier between a number of photons and the brigthness of a pixel in your photo. The implementation of the multiplier is (usually) half-analog and half-digital, but it's still just a multiplier. If you keep the exposure the same, then changing the ISO on a digital camera will NOT introduce any more noise (except for at the extremes of the range, where, for example, analog readout noise may play a role).

This "simulator" artificially adds noise based on the ISO value, as you can easily discover: Set your shutter to 1/500 and your aperture to F8, then switch between ISO 50 and ISO 1600 and look at the letters on the bulb. ISO 50, dark but perfectly readable. ISO 1600, garbled mess. Since the amount of light hitting the simulated sensor stays the same, you should be seeing slightly LESS noise at ISO 1600 (better signal to noise ratio than at low ISO), not more.

edit: To add something genuinely useful: Use whatever mode suits you (manual, Av, Tv) and just use Auto ISO. Expose for the artistic intent and get as much light in as possible (i.e. use a slower shutter speed unless you need to go faster, use a wider aperture unless you need a narrower one). That’s the light that you have, period. Let the camera choose a multiplier (ISO) that will result in a sane brightness range in your JPEG or RAW (you’ll tweak that anyway in post). If the photo ends up too noisy, sorry but there was not enough light.

ISO is an almost useless concept carried over from film cameras where you had to choose, buy and load your brightness multiplier into the camera. Digital cameras can do that on the fly and there’s usually no reason not to let them. (If you can come up with a reason, you probably don’t need this explanation)