1985, Professor barnsley of Georgia Institute of Technology drew the model equation of fern leaf growth for the first time, and put forward the concept of Iterative Function System (IFS) for the first time in mathematics. The following is the first computer-simulated fern feather leaf.
At first glance, this is the same as the real fern feather leaves, but it is really a computer simulation called barnsley fern. Then let's look at the process of computer simulation of this fern.
So let's try to understand this "iterative mode". The overall growth mode of pteridophyte feather leaves is consistent with the growth mode of each leaflet, so the direction of the red box in the figure is the growth mode of pteridophyte feather leaves, and the blue box is the inclination angle of each feather leaf, and the angle of each leaflet is the same, so this is a repeated combination for two times to form pteridophyte feather leaves. Indeed, it's amazing.
We talked a lot about ferns here, but the growth of their feathers is a pattern, which is really amazing. Of course, some people will say that the simulated fern is far from the real fern, so let's take a look at the real barnsley fern.
? Later, the mathematical model also simulated more ferns. Such as Polypodiaceae and Pteridophytes.
Pteridophyte feather leaf model.
Feather leaf model of Polypodiaceae ferns.
? It is true that the secret of plants is beyond our imagination, far beyond our imagination.
? Finally, let's enjoy the fern feather leaves under mathematical simulation. Happy new year to you all!
References:
1.？ Fractal is everywhere, Boston, Massachusetts: Academic Press, 1993.
2. michael barnes Lee, "Variable V Fractal and Hyperfractal".