How can we draw pictures with dots? This is called stippling, which involves putting a lot of dots across an image to approximate tones. On a white background, more (or larger) black dots result in a locally darker image. These two approaches are known as AM and FM stippling. AM – amplitude modulation – means changing the size of each dot as a result of the local image brightness. FM – frequency modulation – means changing the spacing of equal-sized dots. But there’s no need to restrict yourself to purely one or the other.
Here’s Lena with 1996 points, randomly arranged, with the AM approach:
And with 1996 points that have been FM arranged (via Lloyd’s algorithm):
These are extremes of a continuum. For example, the size of the dots could be specified, and an appropriate arrangement found. The header image uses dots that increase in radius from the center of the image.
What about other options? The Voronoi diagrams used so far are isotropic. What about using the gradients of the image to inform the direction of anisotropy? Here are the results of putting the anisotropy parallel and perpendicular to the local gradients:
That gives some interesting structure to the arrangement of dots. For example, the gradient-aligned anisotropy yields sharper edges. This is more evident when there are tons of dots, as with the 8000 in the next example: