Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis
Watching the Daisies Grow: Turing and Fibonacci Phyllotaxis
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观察雏菊的生长：图灵和斐波那契叶序
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发表时间：
2004
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通讯作者：
J. Swinton
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作者：
J. Swinton
图灵在1952年发表的关于形态发生的开创性论文广为人知。不太为人所知的是，他在生命的最后几年里进一步发展了他的形态发生理论，并使用新的计算机来生成反应扩散系统的解。在其他方面，他声称能够解释“斐波纳契叶趋化”现象：植物结构中斐波纳契数的出现。他从未发表过这项工作，但留下了一份几乎完整的关于形态发生和晶格叶序的手稿，以及关于斐波那契叶序的更零碎的注释。我讨论了他提出了许多接近现代思维的关键思想的证据，以及诱人的暗示，他非常接近于用数学方法解释“雏菊”是如何成长为这些模式的。
Turing’s seminal 1952 paper on morphogenesis is widely known. Less well known is that he spent the last few years of his life further developing his morphogenetic theory and using the new computer to generate solutions to reaction-diffusion systems. Among other things, he claimed at one point to be able to explain the phenomenon of “Fibonacci phyllotaxis”: the appearance of Fibonacci numbers in the structures of plants. He never published this work, but did leave a nearly complete manuscript on morphogenesis and lattice phyllotaxis, together with more fragmentary notes on Fibonacci phyllotaxis. I discuss evidence that he developed a number of key ideas close to modern thinking, and tantalising hints that he came very close to a mathematical explanation of how the “daisy grows” into these patterns.