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Optimal transport is art: images to collection of optimally placed particles
Stippling is a kind of drawing style using only points to mimic lines, edges, and grayscale. The entire drawing consists only of dots on a white background. The density of the points gives the impression of grayscale shading.
Back in 1510, stippling was first invented as an engraving technique, and then became popular in many fields because it requires just one color of ink.
Here is a photo of a fine example taken from an exhibition of lithography and copperplate art (the Centenary of European Engraving Exhibition held at the Hubei Museum of Art in March 2015; in case you’re curious, here is the museum’s official page in English).
The art piece is a lithographic print. From a view of one meter away, it shows remarkable detail and appears realistic. However, looking at it from a much closer distance, you can see it’s made up of hundreds of thousands of handcrafted stipples, with the original marble stone giving it even more texture.
From my point of view, this artistic stippling method is like a simulation of variable solidity using small dotted patterns, like a really dense dot matrix printer, except these patterns are handmade. It is fascinating looking at lithographs, observing how a macro reality emerges from uncountable random dots: the mirror reflection on the floor, the soft sense of the cloths, and the mottling on the building engraved by history. (Photos were taken from the same exhibition.)
As a technique invented five hundred years ago, stippling has become popular in so many fields way beyond its original intention because of its simplicity. It was once the standard for technical illustrations, especially in math and mechanics books. Even today, many people are interested in it. Experts from different domains are still using stippling in daily work.
Typical stippling almost always uses one or two colors. Actually, one can create all sorts of textures and tones without introducing artifacts—one cannot achieve both with techniques like hatching or line drawing—just by varying the density and distribution of the dots. That makes stippling an excellent choice when archaeologists, geologists, and biologists are doing fieldwork and want to record things they find immediately. They don’t want to travel along with heavy painting gear; a single pen is good enough for stippling. Even in modern days, compared to photography, stippling still holds some advantages despite requiring a large amount of time. For example, the author can mark and emphasize any features he or she wants right on the drawing; thus, the technique is an important skill—one that is still being taught and researched today.
Here to support my point, I made these dinnertime paper-napkin stipplings (if they look like a complete disaster to you, please forgive me, as I’m not an expert and they only took about five minutes):
It is also very interesting to note that stippling is such a natural way to distribute dense points that the strategy is actually adopted by many living things, like this one in my dish:
In the computer age, there is a special computer graphics domain called non-photorealistic rendering. Stippling is one of its basic artistic painting styles, and can be used as the foundation of many other synthetic styles, such as mosaic, stained glass, hatching, etc.