Thursday, October 29, 2020

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

 

 

 

 

 

 

 

 

 


 

 

 

 

 

Tuesday, October 27, 2020

Campsis gradiflora and Thunbergia gradiflora

Wiki describes this plant as

"

Campsis grandiflora, commonly known as the Chinese trumpet vine, is a fast-growing, deciduous creeper with large, orange, trumpet-shaped flowers in summer. It can grow to a height of 10 meters. A native of East Asia.

I made many sketches of Campsis grandiflora this summer (July - Oct, Hong Kong has a much longer summer season) as I saw this follower first time in Hong Kong since 1995 when I moved to Hong Kong. Orange ones remind me of the time when I encountered this flower in Japan first time long time ago and Shanghai, also first time in China about 5 years ago. Both times the day was a very hot summer day and day time. Usually orange. But I happened to find bluish purple ones in September in Hong Kong. The best sketch is below.




 

 

 

 

 

 

 

 

 

Bluish purple ones




 

















 



After checking I found (actually happened to find) this bluish purple Campsis gradiflora is not Campsis gradiflora but Thunbergia gradiflora and belongs to Acanthacea familiy not to Bigoniaceae family (to which Campsis gradiflora bekongs)


Orange ones (Campsis gradiflora)

 


 

 

 

 

 

 

 

 



 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

AAG