Each scale on an ocellated lizard coordinates its colour with its neighbours.
藍斑蜥蜴身上的每個鱗片都隨著周圍環境變化而變化。
The convoluted pattern on the backs of ocellated lizards is the result of a highly coordinated effort between skin cells.
藍斑蜥蜴背面的複雜迴旋的圖案是皮膚細胞之間高度協調的結果。
As adults, ocellated lizards (Timon lepidus) sport a convoluted pattern of black and green on their backs. Colour patterns aren’t rare in animals, but the ocellated lizard develops its labyrinthine palette in an unusual way.
成年藍斑蜥蜴（學名：Timon lepidus）的背部長著黑色和綠色交錯的複雜圖案。動物身上的彩色圖案中並不罕見，但是這種斑紋蜥蜴具有不尋常的迷宮式顏色變化。
Researchers found that some scales on the lizard’s back change colour during the transformation from juvenile to adult after detecting the colour of neighbouring scales. The team described these scales as decision-making units in a study1 published on 12 April in Nature.
研究人員發現，藍斑蜥蜴在檢測到鄰近鱗片的顏色後在從幼體變形成年的時候，背部的一些鱗片顏色會發生變化。 該團隊認為這些鱗片具有角色功能，並在4月12日的Nature雜誌上發表。
A set of mathematical rules called Turing equations describes how many animals, including lizards, develop stripes or spots. The resulting 'Turing patterns' are continuous across the organism and are determined independently of other biological features, such as lizard scales. But the backs of adult ocellated lizards have a discrete pattern that is linked to individual scales. (The scales on this species are made of clear keratin, so the colours of the underlying skin shine through: each is either black or green.)
一組名為「圖靈方程」的數學規則可以判斷有多少動物，包括蜥蜴是具有條紋或斑點的。這種「圖靈圖案」在整個生物體中是連續的，並且確定獨立於其他生物特徵（例如蜥蜴鱗片）。 但是，成年藍斑蜥蜴的背部根據個體的鱗片會產生不連續的圖案。（這種物種身上的鱗片由清澈的角蛋白製成，所以肌膚底層顏色可以通過：每個都是黑色或綠色）
Self-determination自我決定
To investigate this phenomenon, Michel Milinkovitch, a biophysicist at the University of Geneva in Switzerland, and his colleagues took high-resolution photographs of the backs of three male lizards. The researchers began when the animals were two weeks old and continued until the lizards were three or four years old. The team used the images to track the fates of about 5,000 hexagonal scales across the back of each reptile.
為了調查這一現象，瑞士日內瓦大學的生物物理學家Michel Milinkovitch及其同事拍攝了三隻雄性蜥蜴背部的高清照片。研究人員等到蜥蜴兩周歲時開始試驗，一直到蜥蜴三到四歲。該團隊利用這些圖像跟蹤每個爬行動物身上的約5,000個六角形鱗片的命運。
As each lizard aged, the overall pattern on their backs went from brown with white spots to a convoluted pattern of green and black. Roughly 1,500 scales changed colour, such that green scales had four black and two green neighbours, whereas black scales had three black and three green neighbours. This 『mind the neighbours』 behaviour reminded Milinkovitch of a process called acellular automaton.
隨著每隻蜥蜴年齡增長，它們背部的整體圖案從棕色變為白色、綠色及黑色的交錯的複雜圖案。大約1,500個鱗片顏色發生了變化，綠色鱗片與四個黑色和兩個綠色鱗片相鄰，而黑色鱗片與三個黑色和三個綠色鱗片相鄰。這種注意相鄰鱗片的行為讓Milinkovitch想到了一種叫做無細胞自動化的過程。
Cellular automatons, first described in terms of computer science, are self-replicating units that perform calculations. In ocellated lizards, this means that an individual scale sums up information from the ones around it — how many are black and how many are green — and makes a decision about its own colour.
細胞自動化首先出現在計算機科學方面，用來描述執行計算的自我複製單元。在藍斑蜥蜴中，這意味著個別鱗片總結了周圍的信息 - 有多少是黑色的，有多少是綠色的，然後決定自己的顏色。
Connecting the dots將點連接起來
To find out, the team focused on the lizards』 skin cells. Lizards and fish have skin composed of various cell types that generate different colours. And researchers know that zebrafish skin cells, for example, interact with each other to establish Turing patterns.
為了了解這一點，該團隊開始關注蜥蜴的皮膚細胞。蜥蜴和魚的皮膚具有能夠生成不同顏色的多種細胞類型。研究人員了解到例如斑馬魚皮膚細胞能夠相互之間產生作用以建立圖靈圖案。
Milinkovitch and his team modelled the interactions between colour cells on the basis of equations derived from zebrafish data and compared their results to the patterns on the lizards』 skin. They found that ocellated lizard skin is thick under each scale, which provides room for cells to interact. But between scales, the skin is thin, with less room for cells to connect. The decreased thickness limits the colour to within individual scales on the lizards』 back. This suggests that animal skin bumpiness can disrupt a continuous Turing pattern.
Milinkovitch和他的團隊根據斑馬魚數據得出的方程模擬了彩色細胞之間的相互作用，並將其結果與蜥蜴皮膚上的圖案進行了比較。他們發現，每個鱗片之下的蜥蜴皮膚很厚，為細胞的交互提供了空間。但是鱗片之間的皮膚很薄，細胞連接的空間較小。減小的厚度可以限制蜥蜴背部鱗片的顏色。這表明動物皮膚的顛簸可能會破壞連續的圖靈圖案。
Researchers have shown that cellular automata can create larger Turing patterns, such as those seen on seashells, says Milinkovitch. But the latest study describes the first time that scientists have observed the opposite: small Turing patterns that feed into large cellular automata.
Milinkovitch說，研究人員已經發現細胞自動機可以創建更大的圖靈圖案，如貝殼類似的圖案。但是最新的研究表明科學家第一次觀察到相反的情況：大的細胞自動機產生了小的圖靈圖案。
The development of colour patterns in animals is usually described qualitatively, says Devi Stuart-Fox, an evolutionary biologist at the University of Melbourne in Australia. The ocellated lizard’s patterning probably helps the animal to blend into its environment. 「But when you can show that there are general mathematical principles that can describe biological processes,」 she says, 「it provides a nice conceptual framework to understand what’s happening.」
澳大利亞墨爾本大學的進化生物學家德維·斯圖爾特·福克斯（Devi Stuart-Fox）說，動物的顏色發展模式通常是從總體上講的。藍斑蜥蜴身上的圖案有可能幫助它們融入其環境。「但是，如果有總體數學原理能夠描述生物發展進程的話，」她說，「可以為我們提供很棒的概念框架去解釋發生了什麼。」
Scale 鱗片
Ocellated lizard 藍斑蜥蜴
Convoluted 迴旋的，錯綜複雜的
Labyrinthine 迷路的，迷宮的
Palette 調色板
Transformation 變形
Equation 方程
Pattern 圖案
Biological 生物的
Discrete 不連續的
Keratin 角蛋白
Hexagonal 六邊形的
Overall 整體的
Self-replicate 自我複製
Zebrafish 斑馬魚
本期：迷你數獨
每個謎題都由一個在不同位置給與提示數字的4x4或6x6網格組成。遊戲的目的是將空方格填上數字1到4（對於4x4大小的謎題）或者1到6（對於6x6的謎題），使得每一行，每一列以及每一個宮都沒有重複的數字出現。
本期難度：Diabolical
（答案見下期）
註： 數獨是一種源自 18 世紀末的瑞士數學家歐拉所創造的拉丁方塊遊戲。傳數獨源起於拉丁方陣（ Latin Square ）， 1970 年代在美國發展，改名為數字拼圖（ Number Place ）、之後流傳至日本並發揚光大，以數學智力遊戲智力拼圖遊戲發表。在 1984 年一本遊戲雜誌《パズル通信ニコリ》正式把它命名為數獨，意思是「在每一格只有一個數字」。後來一位前任香港高等法院的紐西蘭籍法官高樂德（ Wayne Gould ）在 1997 年 3 月到日本東京旅遊時，無意中發現了。他首先在英國的《泰晤士報》上發表，不久其他報紙也發表，很快便風靡全英國，之後他用了 6 年時間編寫了電腦程式，並將它放在網站上，使這個遊戲很快在全世界流行。