Why are there so many logarithmic spirals in nature?

Because logarithmic spiral is equiangular, many linear motions are transformed into equiangular spiral motions due to the influence of environment.

Let's take moths to the fire as an example.

For hundreds of millions of years, nocturnal insects like moths have navigated by moonlight and starlight. Because the celestial bodies are far away, these lights are parallel lights and can be used as a reference for straight flight. As shown in the figure below, note that moths can fly in a straight line as long as they fly at a fixed angle, which saves the most energy.

But since humans learned to use fire, these artificial light sources have been very close, and the light appeared in the form of central radiation, so the poor moth began to have bad luck.

Moths think that flying at a fixed angle to light is a linear motion, but the more they fly over the pit, the more they fly into an equiangular spiral and finally fly into the fire. This phenomenon is also called phototaxis of insects by human beings.

The moth said:

Follow your sister's light, fool, staring at the light. I wonder if they will be blind. ! !

We are completely misled by human beings, and the exquisite linear navigation method evolved over hundreds of millions of years has failed because of the interference of human light pollution!

Don't use a guilty moth to put out the veil lamp, convex (#) convex, turn off the light quickly!

Note that the flying insects in the picture below are all doing spiral flight, if the insects have phototaxis. Wouldn't it be better to fly directly?

Don't think that only moths do this. People have the same problem when navigating with a compass.

The fundamental reason is that the parallel field originally used as a reference becomes a central divergent field, which leads to the linear motion becoming a spiral motion.

We also know that there are no absolutely parallel fields in nature, but for the convenience of calculation, we think they are approximately parallel in a small range. If the scale is enlarged and more fields are non-parallel, it is normal that there are a large number of equiangular spirals in nature.

For example, in an ideal state, the fluid should move in a straight line, but under the action of divergent field and the rotation of the earth, it will go out of the shape similar to an equiangular spiral like a moth. The typhoon in the sky and the vortex in the water are formed in this way, but the actual situation is far more complicated than this and can only be considered approximately.

There is also a joke about logarithmic spiral.

The logarithmic spiral was discovered by Descartes in 1638. Jacob Bernoulli also studied it and found many very beautiful features. After various transformations, the result is still the same.

He marveled at and appreciated this beauty, demanding that after his death, his tombstone must be engraved with a logarithmic spiral, and the epitaph was "eadem mutata resurgo".

As a result, the stonemason carved archimedean spiral by mistake, and Jacob's grave knew that he would definitely overturn the coffin!

The Archimedes spiral is like this:

Ordinary people really can't see the difference. Can you see it? Don't be confused!