spent one night reviewing information and writing programs in the morning. This weekend, he did a "dead skin" and made something that is not very like a thing: sunflower seed growth simulation . Take advantage of the heat, and then sacrifice noon time, write some notes.
sunflower seed disk (picture from the Internet)
This article does not intend to explain in detail. This kind of academic approach can be seen in more detail in online search materials, especially professional paid papers. This article only intends to start from the point of view of an amateur trying to popularize science and talk about the few "core articles". In fact, in addition to time becoming more valuable, ability is the eternal and powerful hard constraint!
1. What is the "golden number"? The golden number Φ of
(the fourth sound of Fai) is an irrational number:
golden number
Its reciprocal is:
the reciprocal of the golden number
2. How does the "golden number" come from? In short, the golden number Φ is a quadratic equation: the positive real root of the golden equation
, and the other negative real root is: -1/Φ. More details are omitted in this article.
3. What is the "Golden Horn"? A circle of
is 360 degrees, and the arcs are divided by golden numbers. There are:
q=360°×Φ≈222.49223594996214535365126037163°
p=360°×(1-Φ) ≈ 137.50zzzzz
zz39464634873962837° which people are used to call the inferior angle “p Golden Horn".
4. The role of this article
This article will show in an intuitive way: why certain plants choose the "golden angle" during their growth.
V. Software intuitive simulation
1. Sunflower seed growth simulation animation according to the golden angle Φ:
Sunflower seed growth simulation animation according to the golden angle Φ
2. Sunflower seed growth simulation animation at 138 degrees:
Animation
3. Simulation animation of sunflower seed growth at 137 degrees:
Simulation animation of sunflower seed growth at 137 degrees
4. Simulation animation of sunflower seed growth at 136 degrees:
Simulation animation of sunflower seed growth at 136 degrees
5. Sunflower seeds Simulation animation of growth at 180 degrees:
simulation animation of sunflower seed growth at 180 degrees
6. Simulation animation of sunflower seed growth at 90 degrees:
simulation animation of sunflower seed growth at 90 degrees
7. Simulation of sunflower seed growth at 100 degrees Picture:
sunflower seed growth simulation animation at 100 degrees
8. sunflower seed growth simulation animation at prime 131 degrees:
sunflower seed growth simulation animation at prime 131 degrees
9. sunflower seed growth simulation animation at golden angle:
According to the golden angle linear growth simulation animation of sunflower seeds
, you can see: When the seed growth process is changed to "linear growth" and the growth trajectory still follows the golden angle, the simulation effect can be adjusted better.
6. Intuitive conclusion
sunflower seeds or whorled leaves of plants use golden horns to grow, the purpose is: efficient use of limited living space, try not to leave or leave as little space as possible, so that the sunflower facet is the densest and strongest. In the cruel survival competition, whether it is competing for nutrients, sunshine, growth, and reproduction, it is highly efficient and extremely beneficial. Describe in mathematical language: when the growth process follows the "golden angle", sunflower seeds can beNow the effect of "dense paving" on the plate surface. Viewed from another angle, this kind of "dense paving" is that there are obvious "left-handed spirals" and "right-handed spirals", or called "two sets of positive and negative spirals." When
changes the growth angle, it either obviously grows in a "single spiral", or it grows in a straight line and radially with several equal parts of the circle, resulting in a huge waste of space. Even if 137, 138, or even 137.5, 137.6, which are very close to the golden angle approximate number 137.51, are used, when the number of seeds is large enough, a more obvious "single spiral" will appear. As for the "prime numbers", there are not enough tests. Most of them have common characteristics, only 31. When the number of seeds is 1200, the simulation seems to be good, but it is estimated that it will be worse when the number of seeds increases.
10. Sunflower seeds grow at a prime number 31 degrees simulation animation:
Sunflower seeds grow at a prime number 31 degrees simulation animation
7. Supplementary explanation
Regarding the "golden angle" in plant growth, refer to the Internet search data. It is said that in 1979, the mathematician H. Vogel first simulated the growth of sunflower seeds with a computer, and discovered the best divergence angle of the seeds: the golden angle. In this regard, this article has no originality. The software implementation method used in this article is original.
pays tribute to the true gods from all walks of life! There is no end to learning, and we have a life, everyone encourages.
After remarking the two better parameters, the test is not easy...
Golden angle parameter
prime number 31 parameter
