Beauty of math graphs - 3, Phase plane

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

From: Introduction to Computational Physics
http://astro.physics.ncsu.edu/urca/course_files/Lesson16/index.html  

Some Comments from artistic view points.

1. The first one is most beautiful to me.

Distinct lack and red contrast.
Good composition base on the triangular (just suggesting, not completed)
Mostly Curbs and a little bit straight lines with an arrow. Showing movement explicitly.
Ample space for movement feeling.
A calligraphic flow beauty.

2. The last one is the 2nd best.

Combination of several deformed symmetries - not monotonous symmetries while retain symmetrical beauty.
It shows many small seemingly circular movements as well as some mid size ones in the middle and outer large ones seemingly all connected and combined - showing continuation of flow.

3. The 2nd and 3rd - showing some sketch like incomplete beauty.

4. The beauty is highly likely due to chaos nature as the name of the titles of the two graphs (the1s and the last) - Chaotic Pendulum.

Introduction to Computational Physics says:

"
If chaotic systems where entirely unpredictable, you probably wouldn't have heard so much about them. Their most intriguing features are related to the fact that there are things that can be predicted about these unpredictable systems.

 "

AGG