Most modern land plants grow leaves in a spiralling pattern where their angles in relation to one another settle on the “golden ratio” derived from the famous Fibonacci sequence – a set of numbers where each is the sum of the two preceding ones, as in 1, 1, 2, 3, 5 and so on. From flowering artichokes to pine cones, the pattern appears in more than 91 per cent of land plants today.

大多数现代陆地植物的叶子呈螺旋状生长，它们彼此之间的角度遵循于著名的斐波那契数列的“黄金比例”，其中每个是前两个的和，如1,1,2,3,5等等。从开花的洋蓟到松果，如今超过91%的陆地植物都是这种模式。

“Lots of things you’re familiar with, if you look at them in detail, you’ll actually find evidence of Fibonacci spirals,” says Sandy Hetherington at the University of Edinburgh in the UK.
英国爱丁堡大学(University of Edinburgh)的桑迪·赫瑟林顿(Sandy Hetherington)说:“很多你熟悉的东西，如果仔细观察，你实际上都会发现斐波那契螺旋的证据。”

To investigate if the earliest land plants followed this same rule, Hetherington and his colleagues examined fossils that had been extracted from a sediment deposit called Rhynie Chert in Scotland. They chose fossils of one of the oldest leafy species preserved: the club moss Asteroxylon mackiei, which grew during the Devonian Period, 400 million years ago.
为了研究最早的陆地植物是否遵循同样的规律，赫瑟林顿和他的同事们检查了从苏格兰一个名为Rhynie Chert的沉积物中提取的化石。他们选择了保存最古老的叶类物种之一:生长在 4 亿年前泥盆纪时期的球杉科植物 Asteroxylon mackiei 的化石。

The team digitally layered thin slices of the fossils – one of which had been collected over 100 years ago – into a 3D reconstruction. The model revealed a diverse set of swirls, whorls and spirals in A. mackiei’s leaves.
该团队用数字技术将化石薄片分层，其中一个化石已经收集了100多年，并生成了一个三维重建模型。该模型揭示了mackiei化石叶子上多样的螺旋、轮廓和螺线形状。

“I went into this investigation assuming that we were going to find Fibonacci spirals there,” says Hetherington. “It really came as a shock.”
赫瑟林顿说:“我最初以为我们会在那里找到斐波那契螺旋，”“结果真的是出乎意料。”

The unusual structure suggests, contrary to many botanists’ previous assumptions, that leafy plants didn’t necessarily start out growing leaves following the Fibonacci pattern. Instead, they appear to have evolved to follow that rule over the past few hundred million years. Some modern club mosses related to A. mackiei also have non-Fibonacci spirals, so the trait hasn’t been entirely lost.
与许多植物学家之前的假设相反，这种不寻常的结构表明，叶类植物并不一定是按照斐波那契模式开始长叶子的。相反，它们似乎在过去几亿年间逐渐进化出这种规律。一些与mackiei有亲缘关系的现代球杉类植物也有非斐波那契螺旋，所以这种特征并没有完全消失。

Because fossils of other kinds of primitive plants are often missing key parts of their stem or leaves, “looking at these rosette-type fossils was an extremely good idea”, says Jonathan Swinton at a Deodands, a private scientific consultancy in the UK. The finding “sets up a really interesting opportunity for interactions between mathematicians and biologists”, he says.
英国私人科学咨询公司Deodands的乔纳森•斯文顿(Jonathan Swinton)表示，由于其他种类的原始植物化石往往缺少茎或叶的关键部分，“研究这些莲座型化石是一个非常好的想法””。他说，这一发现“为数学家和生物学家之间的互动提供了一个非常有趣的机会”。

Researchers still don’t know why so many plants have leaves that follow the Fibonacci spiral, but some speculate that it is their way of maximising the amount of sunlight that hits each leaf.
研究人员仍不知道为什么如此多的植物叶子遵循斐波那契螺旋，但一些人推测，这可能是它们最大限度地利用阳光照射每个叶子的方式。