It took an evening to review the materials, a morning to write a program, and this weekend to do a "dead skin" and make something that doesn't look like a thing: a sunflower seed growth simulation. Take advantage of the heat, sacrifice the noon time, and write some text to record.
Sunflower seed flower tray (image from the Internet)
This article is not intended to be laid out in detail, such academic practices, in the internet search information, especially professional paid papers, can be seen in more detail. This article only intends to start from the perspective of an amateur trying to popularize science, and say a few "core dry articles". In fact, in addition to the increasing value of time, ability is an eternal and powerful hard constraint!
<h1 class="pgc-h-arrow-right" >. </h1>
The gold number Φ (fai fourth sound) is an irrational number:
The number of gold
Its reciprocal is:
The reciprocal of the number of gold
<h1 class="pgc-h-arrow-right" >2, where did the "golden number" come from? </h1>
In short, the gold number Φ is a quadratic equation:
The Golden Equation
Of the positive solid root, the other negative solid root is: -1/Φ. More details are omitted from this article.
<h1 class="pgc-h-arrow-right" >3. What is the "Golden Horn"? </h1>
A circumference is 360 degrees, with a golden number dividing the arc, which has:
q=360°×F≈222.49223594996214535365126037163°
p=360°×(1-F)≈137.50776405003785464634873962837°
Customarily, people refer to inferior angle p as the "golden horn".
<h1 class="pgc-h-arrow-right" >4</h1>
This article will show in a visual way why some plants choose the "Golden Horn" during their growth process.
<h1 class="pgc-h-arrow-right" >5, software intuitive simulation</h1>
1. Simulated GIF of sunflower seeds growing by golden horn Φ:
Sunflower seeds grow by golden horn Φ simulated GIF
2. Simulated GIF of sunflower seeds growing at 138 degrees:
Simulated GIF of sunflower seeds growing at 138 degrees
3. Simulated GIF of sunflower seeds growing at 137 degrees:
Simulated GIF of sunflower seeds growing at 137 degrees
4. Simulated GIF of sunflower seeds growing at 136 degrees:
Simulated GIF of sunflower seeds growing at 136 degrees
5. Simulated GIF of sunflower seeds growing at 180 degrees:
Simulated GIF of sunflower seeds growing at 180 degrees
6. Simulated GIF of sunflower seeds growing at 90 degrees:
Simulated GIF of sunflower seeds growing at 90 degrees
7. Simulated GIF of sunflower seeds growing at 100 degrees:
Simulated GIF of sunflower seeds growing at 100 degrees
8. Simulated GIF of sunflower seeds growing at 131 degrees of prime:
Simulated GIF of sunflower seeds growing at 131 degrees prime
9. Simulated ANIMATION OF SUNFLOWER SEEDS Growing Linearly by Golden Horn:
Simulated GIF of sunflower seeds growing linearly at the golden horn
It can be seen that when the seed growth process is changed to "linear growth", the growth trajectory still follows the golden horn, and the simulation effect can be adjusted to better.
< h1 class= "pgc-h-arrow-right" > six intuitive conclusions</h1>
The reason why the rotational leaves of sunflower seeds or plants are grown with the golden horn is to efficiently use the limited living space and leave as little or as little space as possible, so that the sunflower flower disc is the densest and strongest. In the cruel competition for survival, whether it is to compete for nutrients, sunshine, or growth and reproduction, it is efficient and extremely advantageous. Described in mathematical terms: When the growth process follows the "golden horn", sunflower seeds can achieve the effect of "dense paving" of the plate surface. This kind of "dense paving" is observed from another point of view, that is, there are obvious "left spirals" and "right spirals", or called "two sets of positive and negative spirals".
When the growth angle is changed, either it is obviously grown in a "single spiral", or it grows in a number of equal circles and grows radially in a straight line, resulting in a huge waste of space. Even with 137, 138, or even 137.5, 137.6, which are very close to the approximate golden angle of 137.51, a more obvious "single spiral" will appear when the number of seeds is large enough. As for the "prime numbers", they are not tested enough, most of them have ordinary characteristics, only 31, and at the seed number of 1200, it seems to be a good simulation, but it is estimated that it will be worse after the number of seeds increases.
10. Simulated GIF of sunflower seeds growing at 31 degrees of prime:
Simulated GIF of sunflower seeds growing at 31 degrees prime
<h1 class="pgc-h-arrow-right" >7</h1>
Regarding the "golden horn" in plant growth, learn from the network search data. It is said that in 1979, mathematician H. Vogel originally simulated the growth of sunflower seeds by computer, and the study found the best divergence angle of seeds: the golden horn. In this regard, this article is not original. The software implementation used in this article is original.
Hats off to all the true gods! There is no end to learning, and I have an end in life, and everyone encourages me.
After the text, note two sets of better parameters, the test is not easy ah...
Golden Horn parameter
Prime number 31 parameter