貢中元的部落格

Unlimited number of periodic decagonal tiling  with a2-D atom sites quasi crystal model貢中元chung yuan kung

Unlimited number of periodic decagonal tiling (2D-crystal)

The fat and thin rhombus tiles with different acute angles of 36 and 72 degrees  can combine to form six different decagonal tiles, of different inner structures, Each decagons composed of ten rhombuses , five thin rhombus and five fat rhombus , where a, b, c, d, e, f, are marked for six different decagons respectively in Figure 1.  For the fat rhombus in the decagons of type-a, type-d, type-e and type-f are highlighted in red, purple red, yellow, and light blue, respectively. These six decagons which can be regarded (considered) as basic unit, instead of two types of rhombuses, to fabricate (infinity) tiles in this paper. And be noted that only type-a decagonal tile is five-fold symmetric and the rest decagons are only mirror symmetric.

 When I attend my 50 year anniversary, I asked physics dept to give a speech abot Penrose tiling. Because during Covid 19 mperiod, a  I afraid use public transpotation may have chance to be get influence infection and affect to my 99 year old mother. at that day  I drove my car by myself with a poor  eye seeing. 

是，所有六個十邊形都在一個彭羅斯瓷磚中，沒有缺陷，並且有很大的潛力擴展到無限而不產生缺陷。.

75歲自序  字祚自壽

從十多年前在電腦前, 從一張照片改製第一張圖畫開始，我就自以為是無師自通、自作自授的畫家。得到最友善最佳的評語，「抽象的莫名其妙」，不知作品好歹的自稱畫家, 還默默地參加了幾次畫展。後來還真的自作自售，賣出了一批友情贊助的畫作。在電腦前面是有各種不同的學習研究工作的, 也要常常注意到學生的論文進展。多年來, 晨昏顛倒,樂此(電腦)不疲。一時興起又恣作眥受恣意畫了許多號稱超級抽象，自己也看不懂的作品。

銳角為15,30,45,60,75,90度的菱形鑲嵌作圖,, 並可以延伸到無限大.

下列!只是初期示範,,,, 後續變化更趨雜複,‧勢必使用電腦軟体技術‧

無極生有極,有極變太極    推手  本文只是個問號? cykung 貢中元

這張圖找不到原始檔,這些圖‧我現在也畫不出來了!opt art only, 與下文無必然關係!!

道瓊悲歌  道道道 非常道 窮非瓊  非常窮    懵然回首 但見牛骨一幅掛牆頭 (晒街頭)

(怯)且問金牛何處尋, 熊齒洌洌 笑春風

two dimensional Unit cell of infinite size 二維無限大的晶胞 all these can be extended to infinite

He is happy 

謝謝大家照顧,貢校長最後幾年是很幸福快樂, 沒有太多病痛

OPT 歐普幾何鋪磚(tiling)藝術, 有些圖似乎是從來未見過的-C.Y.KUNG貢中元

這張圖是有一邊比另一邊稍微突出的錯覺,但是每個人的眼睛不同,因為不容易說明問題的動機,目前統計上無法得到結論. 如果可以的話,請告知左邊較突或是右邊