Dithering in its simplest form can be understood by observing what happens when we quantise an image with and without modifying the source by random perturbation. In the examples below, a gradient of 256 grey levels is quantised to just black and white. Note how the dithered gradient is able to simulate a smooth transition from start to end.
The image of Earth from Space captivated the World
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for (int gap = n / 2; gap 0; gap /= 2) {