Butterfly Curve

Yesterday, I was so boring and just finished the work assigned from professor. Surfed the internet and found out this beautiful equations on Wikipedia; then I used Matlab to write the codes........It is beautiful, isn't it? Amazing sine, cosine and exponential !

This is Butterfly Curve, made by 2 parameter equations:
x = sin (t)(e^{cos (t)}-2cos (4t)-sin⁵ (t/12))

y = cos (t)(e^{cos (t)}-2cos (4t)-sin⁵ (t/12))

or by polar equation:

r = e^sinθ-2cos (4θ)+sinθ⁵ (2θ- π/24)

The right side is "Heart Curve", just add some scalars on equations then you can get this beautiful picture.

Ps: Parameter "t", I used t= 20π generated 20000 points.

Forest of Shadows/ Wish, Submission

from album: Where dreams turn to dust (2001)　

　

Forest of Shadows, another depressive doom metal band I like. Unlike "Warning" from U.K., "Forest of Shadows" performs the feelings of extremely sadness, lost hoping and grief in their rhythms. "Warning" uses the vocal instead, while their music is more like "old school" doom metal style. When I listen to F.O.S., I think there includes some senses of awe to Nature.

from album: Six Waves of Woe (2008)

Blind Guardian/ Dead Winter Reigns

Blind Guardian, they have an album called: "Night fall in the Middle-earth" was a tribute to LOTR. This is my favorite album, because once I was a big fan of LOTR, and also a speed metal head.When I was getting deeper in metal music, I found there are many tribute bands of LOTR (mostly, I focus on black metal's part), such as: Burzum, Summoning......etc. They also got the ispiration from Nordic Mythology, you can find it from their many works.

Ps: Even now I stop reading LOTR's novel, I am still sometimes listen to those tribute CDs.

Uaral/ Depression

This is one of my favorite bands from Chile. Their style is doom/ depressive metal (I am not sure if my classification is correct.) But it's not the point. Listen to music is.......

Some Dramas I've watched lately

I've seen many dramas lately, some were made me cried, some laughed and some warmed my heart.

Seen "The Reader", cried out loud.
For one part of the movie, main actress trying hard learning reading for her lover. My tears to her with positive feelings, I was happy for her. Although it's not a happy ending.

Seen "Beautiful Mind", I was also cried for the role of John Nash.
Cried for him stuck in the bottle of neck about his research, recalled that I ever suffered as the same situations. Cried for the same feelings, cried for the same reasons.

Seen "The Legend of Eileen Chang", my sadness for her late life, loneliness. And also for feeling unfair comments upon Eileen Chang's characters by other people.

Was her late life exactly such miserable as the drama showed it?

How colorful of her life she ever had..........

Warning/ Watching from a distance

最近又覺得這首歌很棒了，不過聽的心情不一樣，不像之前邊聽邊難過。


當時是一個音樂同好傳給我的。那時還在念碩士，其實日子很苦悶，研究沒有進展，經常失眠。一開始聽只覺得旋律相當相當的哀傷，並沒有非常仔細聽歌詞，直到有天突然醒悟一份已逝的舊情；這才去找詞來看。看完之後感覺更強烈，竟也跟著唱起來最後還掉眼淚。


每次聽到特別有感觸的歌曲，我都會把它翻成中文，也順便練習一下自己的英翻。


（欲看歌詞及翻譯請按 read more...）


【註】

• youtube真貼心，提供幾個尺寸的視窗比例。還有外框顏色可以選擇呢！以前都是自己調比例的。原版有12多分鐘，這個版本是有刪減的，不過歌詞有唱完。

知識焦慮症候群

人都是有好奇心的，面對未知的事物總是會想好好的瞭解一番。

我二哥是一個學者，平常總是一副閒逸的模樣，跟人對談或是思考問題的時候看起來就是那樣不疾不徐。有一天我告訴他一個網站，說是可以讓他查閱自己發表論文的被引用次數以及那些人引用過，而非SCI線上版本。可追溯到90年代的文章。他要我E-MAIL給他那個網站，半天過後，他寄來一封語氣急促的回信說：「我看不懂這個網站怎麼用！ 如果只是要查找論文，幹嘛不用GOOGLE？你有TITLE了！不過這兩個期刊我們學校沒有訂閱......」

我回：「當然，如果是找文章，GOOGLE好用多了，這是用來查引用的。」一分鐘之後，他立馬回信：「喔我懂了！」

記得以前曾經問過他一個數學問題，那是一種把實數變成復數的轉換函數，他聽了我的描述之後，不甚了解，又要我拿書本來給他看，就這麼研究了一兩個小時後走過來教我，我懂了之後他說了一句很妙的話：「唉呀！哪來那麼多函數啊！？」等到有天我在書架上發現一本「特殊函數概論」（那是姊姊的）時心想：「原來有那麼多函數啊？！」

又有一天，哥哥說了一句妙話：「啊！你們學工程的，符號都亂用，大拍（Π）是連乘也被你們拿來表示函數符號了！」我當下實在想不出有什麼不錯的話反駁，只好說：「你們物理的，老是在談論這個東西有沒有『物理意義』，難道沒有物理意義就代表沒有意義？」那時候正好看到一篇文章講數學家調侃物理學家的內容，就把它拿來用了。

現在我想大概是我們的符號系統還不夠健全吧？

【註】
1. 二哥在大學教物理。
2. SCI線上版本收錄2000年以後的文章，之前的必須使用光碟版。
3. SCI是路透社的資料庫，頗具權威性，台灣學界似乎很重視來自這個單位的引用。