Countershading, or Thayer's law, is a method of camouflage in which an animal's coloration is darker on the top or upper side and lighter on the underside of the body. This pattern is found in many species of mammals, reptiles, birds, fish, and insects, both in predators and in prey.

When light falls from above on a uniformly coloured three-dimensional object such as a sphere, it makes the upper side appear lighter and the underside darker, grading from one to the other. This pattern of light and shade makes the object appear solid, and therefore easier to detect. The classical form of countershading, discovered in 1909 by the artist Abbott Handerson Thayer, works by counterbalancing the effects of self-shadowing, again typically with grading from dark to light. In theory this could be useful for military camouflage, but in practice it has rarely been applied, despite the best efforts of Thayer and, later, in the Second World War, of the zoologist Hugh Cott.

The precise function of various patterns of animal coloration that have been called countershading has been debated by zoologists such as Hannah Rowland (2009), with the suggestion that there may be multiple functions including flattening and background matching when viewed from the side; background matching when viewed from above or below, implying separate colour schemes for the top and bottom surfaces; outline obliteration from above; and a variety of other largely untested non-camouflage theories. A related mechanism, counter-illumination, adds the creation of light by bioluminescence or lamps to match the actual brightness of a background. Counter-illumination camouflage is common in marine organisms such as squid. It has been studied up to the prototype stage for military use in ships and aircraft, but it too has rarely or never been used in warfare.

The reverse of countershading, with the belly pigmented darker than the back, enhances contrast and so makes animals more conspicuous. It is found in animals that can defend themselves, such as skunks. The pattern is used both in startle or deimatic displays and as a signal to warn off experienced predators. However, animals that habitually live upside-down but lack strong defences, such as the Nile catfish and the Luna moth caterpillar, have upside-down countershading for camouflage.

The English zoologist Edward Bagnall Poulton, author of The Colours of Animals (1890) discovered the countershading of various insects, including the pupa or chrysalis of the purple emperor butterfly, Apatura iris, the caterpillar larvae of the brimstone moth, Opisthograptis luteolata and of the peppered moth, Biston betularia. However he did not use the term countershading, nor did he suggest that the effect occurred widely.

The New Hampshire artist Abbott Handerson Thayer was one of the first to study and write about countershading. In his 1909 book Concealing-Coloration in the Animal Kingdom, he correctly described and illustrated countershading with photographs and paintings, but wrongly claimed that almost all animals are countershaded. For this reason countershading is sometimes called Thayer's law. Thayer wrote:

Animals are painted by Nature darkest on those parts which tend to be most lighted by the sky's light, and vice versa. ... the fact that a vast majority of creatures of the whole animal kingdom wear this gradation, developed to an exquisitely minute degree, and are famous for being hard to see in their homes, speaks for itself.

— Thayer

Thayer observed and painted a number of examples, including the Luna moth caterpillar Actias luna, both in its habitual upside-down feeding position, where its countershading makes it appear flat, and artificially inverted from that position, where sunlight and its inverted countershading combine to make it appear heavily shaded and therefore solid. Thayer obtained a patent in 1902 to paint warships, both submarines and surface ships, using countershading, but failed to convince the US Navy to adopt his ideas.

Hugh Bamford Cott in his 1940 book Adaptive Coloration in Animals described many instances of countershading, following Thayer in general approach but criticising Thayer's excessive claim ("He says 'All patterns and colors whatsoever of all animals that ever prey or are preyed upon are under certain normal circumstances obliterative.'") that effectively all animals are camouflaged with countershading. Cott called this "Thayer straining the theory to a fantastic extreme".

Both Thayer and Cott included in their books photographs of a non-countershaded white cockerel against a white background, to make the point that in Thayer's words "a monochrome object can not be 'obliterated', no matter what its background" or in Cott's words "Colour resemblance alone is not sufficient to afford concealment". Cott explained that

Contrary to what might have been expected by any one lacking in artistic perception, the bird appears highly conspicuous, the back looking lighter, and the breast darker, than the background, although in actual fact, back, background and breast are all pure white."

Countershading is observed in a wide range of animal groups, both terrestrial, such as deer, and marine, such as sharks. It is the basis of camouflage in both predators and prey. It is used alongside other forms of camouflage including colour matching and disruptive coloration. Among predatory fish, the gray snapper, Lutianus griseus, is effectively flattened by its countershading, while it hunts an "almost invisible" prey, the hardhead silverside, Atherina laticeps which swims over greyish sands. Other countershaded marine animals include blue shark, herring, and dolphin; while fish such as the mackerel and sergeant fish are both countershaded and patterned with stripes or spots.

It tones the canvas on which are painted the Leopard's spots, the Tiger's stripes ... It is the dress almost universally worn by rodents... It is the essential uniform adopted by Conies, Asses, Antelopes, Deer ... It is repeated extensively among the marsupials ... It provides a basic livery for the great majority of snakes, lizards, and amphibians. Among insects it reaches a fine state of perfection in different caterpillars and grasshoppers. ... It is, however, in rivers, and in the surface waters of the sea, that countershading reaches its maximum development and significance.

— Hugh Cott

Mesozoic marine reptiles had countershading. Fossilised skin pigmented with dark-coloured eumelanin reveals that ichthyosaurs, leatherback turtles and mosasaurs had dark backs and light bellies. The ornithischian dinosaur Psittacosaurus similarly appears to have been countershaded, implying that its predators detected their prey by deducing shape from shading. Modelling suggests further that the dinosaur was optimally countershaded for a closed habitat such as a forest.

Another form of animal camouflage uses bioluminescence to increase the average brightness of an animal to match the brightness of the background. This is called counter-illumination. It is common in mid-water pelagic fish and invertebrates especially squid. It makes the counter-illuminated animal practically invisible to predators viewing it from below. As such, counter-illumination camouflage can be seen as an extension beyond what countershading can achieve. Where countershading only paints out shadows, counter-illumination can add in actual lights, permitting effective camouflage in changing conditions, including where the background is bright enough to make an animal that is not counter-illuminated appear as a shadow.

Countershading, like counter-illumination, has rarely been applied in practice for military camouflage, though not because military authorities were unaware of it. Both Abbott Thayer in the First World War and Hugh Cott in the Second World War proposed countershading to their countries' armed forces. They each demonstrated the effectiveness of countershading, without succeeding in persuading their armed forces to adopt the technique, though they influenced military adoption of camouflage in general.

Cott was a protege of John Graham Kerr who had quarrelled with Norman Wilkinson in the First World War about dazzle camouflage for ships. Wilkinson remained influential in 1939 as an inspector of camouflage, so a political argument developed. Cott was invited to camouflage a 12-inch rail-mounted gun, alongside a similar gun camouflaged conventionally. Cott carefully combined disruptive contrast to break up the gun barrel's outlines with countershading to flatten out its appearance as a solid cylinder. The guns were then photographed from the air from various angles, and in Peter Forbes's view "the results were remarkable." Cott's gun is "invisible except to the most minute scrutiny by someone who knows exactly where to look and what to look for. The other gun is always highly visible." The authorities hesitated, appearing to be embarrassed by the evidence that Cott was right, and argued that countershading would be too difficult to use as an expert zoologist would be needed to supervise every installation. Cott was posted to the Middle East, and Kerr unsuccessfully intervened, pleading for guns to be painted Cott's way and Cott to be brought home.

The Australian zoologist William Dakin in his 1941 book The Art of Camouflage followed Thayer in describing countershading in some detail, and the book was reprinted as a military handbook in 1942. Dakin photographed model birds, much as Thayer and Cott had done, and argued that the shoulders and arms of battledress should be countershaded.

Countershading was described in the US War Department's 1943 Principles of Camouflage, where after four paragraphs of theory and one on its use in nature, the advice given is that:

Upper surfaces should be painted and textured so as to conform to the color and tone of the surrounding country (background) and the sides graded and toned from this to the white which the under surfaces and parts in shade should be painted.

Inventors have continued to advocate military usage of countershading, with for example a 2005 US patent for personal camouflage including countershading in the form of "statistical countercoloring" with varying sizes of rounded dark patches on a lighter ground.

Research by Ariel Tankus and Yehezkel Yeshurun investigating "camouflage breaking", the automated detection of objects such as tanks, showed that analysing images for convexity by looking for graded shadows can "break very strong camouflage, which might delude even human viewers." More precisely, images are searched for places where the gradient of brightness crosses zero, such as the line where a shadow stops becoming darker and starts to become lighter again. The technique defeated camouflage using disruption of edges, but the authors observed that animals with Thayer countershading are using "counter-measures to convexity based detectors", which implied "predators who use convexity based detectors."

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  Rail-mounted guns countershaded by Hugh Cott (top) and conventionally camouflaged (middle), August 1940. The British authorities agreed Cott's countershading worked, but refused to adopt it.
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  BL 7.2-inch howitzer with countershaded barrel, September 1944
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  A preserved Sherman Firefly; its gun barrel is countershaded and disruptively patterned to disguise its length.
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  True (graduated from dark to light) countershaded Focke-Wulf Fw 190

Hannah Rowland, reviewing countershading 100 years after Abbott Thayer, observed that countershading, which she defines as "darker pigmentation on those surfaces exposed to the most lighting" is a common but poorly understood aspect of animal coloration. She noted there had been "much debate" about how countershading works. She considered the evidence for Thayer's theory that this acts as camouflage "by reducing ventral shadowing", and reviewed alternative explanations for countershading.

Camouflage theories of countershading, Rowland wrote, include "self-shadow concealment which results in improved background matching when viewed from the side"; "self-shadow concealment that flattens the form when viewed from the side"; "background matching when viewed from above or below"; and "body outline obliteration when viewed from above". These are examined in turn below.