Similarly, zebras, leopards, tigers, Holstein cows, clown fish, golden ring snakes and silver ring snakes all follow the same equation. If you want to know the specific biological mechanism, please see the following documents 4 and 5.
At the suggestion of @ Lin Yuan, the specific explanation in Reference 2 is added: "In the animal embryo stage, a chemical called morphogenetic substance forms a certain spatial morphological distribution on the embryo surface in a dynamic system of reaction and diffusion, and then in the subsequent cell differentiation, morphogenetic agents contribute to the formation of melanin, and the uneven distribution of morphogenetic agents is also produced. Here, the reaction-diffusion equation is defined on a slightly flat cylindrical surface (animal skin) plus a long cylindrical surface (tail). In the formula, the characteristic function of Laplace operator on the cylindrical surface is the product of cosine functions in two directions, that is, cos(nx/a)cos(2my/b), where A and B are animal body length and "waist circumference" respectively, M and N are natural numbers or zero, and X and Y are two directional variables. The most important thing is the ratio of A to B. When a/b is not too large or too small, both directions are easy to appear in the characteristic function, so the pattern tends to be speckle. When a/b is large or small, the characteristic function is easily a cosine function in one direction, and the pattern is a stripe. Through such a simple analysis, we can get two "theorems" in biology:
"Theorem 1": The skin of snakes is always striped, and there are few spots. Friends who don't believe this rule may wish to find some pictures of snakes to verify. Famous poisonous snakes such as golden ring snake and silver ring snake are typical striped skins. Mathematically speaking, the snake is the best example of an animal with a large ratio of length to width. In addition, according to the same reason, the stripes of snakes are mostly horizontal and rarely vertical.
Theorem 2: There are only animals with striped tails and spotted bodies in the world, and there are no animals with striped tails and striped bodies. What everyone sees is the Northeast Tiger with stripes on its tail, the leopard with spots on its tail, the cheetah with a tattoo and spots on its tail, but the animal without stripes on its tail!
Related literature:
1 zebra, zebra-black spots on white background &; White dots on a black background? 20 1 1-05-06
2 pdf: Talking about Biomathematics and Pattern Generation Shi Junping's Science, page 6, global-sci. , org in 2005.
3 ppt: Mode and Reaction-Diffusion System, Larry Shlu, Hu Wenyong, Li Weishen, Sun Yat-sen University, 20 12, simwe.com's page.
Bmp-Sox9-Wnt Turing Network Modulated by Morpheme Gradient,< Science & gt 1 20 14.
5 Developmental Biology Online 10e: Mathematics of Models
Turing's theory of biological pattern formation has been proved by experiments.
The formation of fingers and toes also conforms to Turing's biological model theory. Science and technology daily 2065438+August 4, 2004.