看了部纪录片 BBC.The.Secret.Life.of.Chaos ，几段话值得摘录。

Turning太伟大了，没想到在生物和化学上的造诣那么高

This is a film about one very simple question. How did we get here?

The natural world really is one great, blooming, buzzing confusion. It's a mess of quirky shapes and blotches. What patterns there are, are never quite regular, and never seem to repeat exactly.

but math & science do. e.g. the triangle are always the same, with same property. the atoms are universally the same)

But code breaking was just one aspect of Turing's genius. Just one part of his uncanny ability to see patterns that are hidden from the rest of us. For Turing, the natural world offered up the ultimate codes. And over the course of his life he'd come tantalisingly close to cracking them.

And he had realised that there was this possibility that simple mathematical equations might describe aspects of the biological world.
and later in Turing's life, an even more radical idea. The idea that a simple mathematical description could be given for a mysterious process that takes place in an embryo. The process is called morphogenesis, and it's very puzzling. At first, all the cells in the embryo are identical. Then, as this footage of a fish embryo shows, the cells begin to clump together, and also become different from each other.

Morphogenesis is a spectacular example of something called self-organisation.

The Chemical Basis of Morphogenesis - The sheer chutzpah of this paper was staggering.

like Alan Turing, Mandelbrot had a gift for seeing nature's hidden patterns. He could see rules where the rest of us see anarchy. He could see form and structure, where the rest of us just see a shapeless mess.


In essence, Turing's equations described something quite familiar, but which no-one had thought of in the context of biology before. Think of the way a steady wind blowing across sand creates all kinds of shapes. The grains self-organise into ripples, waves and dunes. This happens, even though the grains are virtually identical, and have no knowledge of the shapes they become part of. Turing argued that in a very similar way, chemicals seeping across an embryo might cause its cells to self-organise into different organs.

沙丘的比喻太深刻了！

So, an area where mathematics had never been used before, pattern formation in biology, animal markings,

里面提到的BZ reaction，没想到居然也是self-organize的一种啊。赞啊赞

chaos理论四位开山祖师：Turning, Belousov, Lorenz, Mandelbrot

才反映过来纯self-reference也是一种void啊