貢中元的部落格

祝彭羅斯瓷磚發現五十週年  Celebrating the fiftieth anniversary of the discovery of the Penrose tile cykung

Penrose Kung Cluster coupling  to a defect free infinite size tessellation 耦合到無缺陷的無限尺寸鑲嵌cykung,貢中元

由於視力不佳，中文字有很多錯誤，敬請諒解

second kind of impossible! With a coupling

這是一個精心製作的無可挑剔的Penose圖案耦合傑作，其重點是同一個Penrose圖上五個正五邊形結構体和六個正五邊形結構体的緊密共同出現

圖 5 顯示圖 4 的一個角已被轉移到五個正五角結構，同理所有其他六個正五角結構可以轉變成所有五個正五角結構，和上述的手法一樣所有五個正五角結構一樣，可以同時轉化為所有六個正五角結構

This following picture is an impeccably crafted masterpiece of Penose pattern coupling, focusing on the close co-occurrence of five regular pentagonal structures and six regular pentagonal structures on the same Penrose diagram..  The figure below is a perfect masterpiece of Penose mode coupling, focusing on the tight co-occurrence of five regular pentagonal structures and six regular pentagonal structures on the same Penrose diagram.  One corner of Figure 4 has been transferred to five regular pentagonal structures,So by the same token all other six regular pentagonal structures can be transferred to all five regular pentagonal structures, and likewise all five regular pentagonal structures can be transferred to all five regular pentagonal structures,

This book has something to do with Penrose's great paving map, and also with the quasi crystal. It's a very interesting scientific discovery travelling but the title completely msde memisunderstood, and it's easy to ask What is the only kind bt just see the title of book for a retired lazy Professor? This is iIn the end to my mind keeping asked what is the only kind?  which one is only kind?? It should be the most original  Penrosetiling. Turning an angle of 72 degrees can return to the original point... Since the Spring Festival  this year (2022), I have been looking for self-righteousness and Penrose by mistake. In the end which one is only kind?? It should be the most positive Penrose Penrose diagram. Turning an angle of 72 degrees can return to the original point... Since the Spring Festival this year (2022), I have been looking for a  very opininated (self-righteousness)   Penrose tiles  by mistake.(musunderstiid only kind . The Penrose tiles of many only kinds! which I was afraid to count them as second kind! or of the different  kind, -‧ completely misunderstood the original intention of Paul Steinhart, mistakenly hiting the wrong point , and  now I thought it was second possible, and also defined a drawing specification by starting from the most original six decagins and  standardized a rule{examples) of ciupling and then it can be drawn the infinity different types to a infinity insize.

慶祝彭羅斯瓷磚發現五十週年  Celebrating the fiftieth anniversary of the discovery of the Penrose tile cykung

Penrose Kung Cluster coupling  to a defect free infinite size tessellation 耦合到無缺陷的無限尺寸鑲嵌cykung,貢中元

這本書與Penrose 的偉大鋪磚圖有關, 也與quasi crystal 有關. 是一本很有-趣的科學發掘過程  但是書名卻讓我完全誤解,很容易不由得問道•What is the only kind?  這是到底那一種是only kind??應該就是最正的五重性 Penrose 潘若斯圖,轉72度角可以回到原點…從今年春節 (2022)我就誤打誤撞的去找自以為是與 Penrose 不一樣的 second kind 的Penrose 圖,, -‧完全誤斛Paul steinhart的原意,誤 打誤撞, 自以為 second possible,, 也自行定義了一此作圖規範`然後可以畫出可推衍到無限大的晶胞結構,有五重旋轉對稱性,也有類平移對稱性..我用上化學的簇來命名這種最小的晶胞結構  ,,如果我有機會寫這本書的話,, 我會引用誤 打誤撞,是會走出另一種可能的. 自以為是的 second  kind possible...就算是對自己未求是甚解, 盲目冒追,,,,進,,  或訐再引用   書中的一句話 「,If one can expose the underlying assumptions and find a long-overlooked loophole, the second kind of impossible is a potential gold mine that can offer a scientist the rare opportunity, perhaps a once-in-a-lifetime opportunity, to make a transformational discovery」如果一個人能夠揭露潛在的假設並找到一個長期被忽視的漏洞，那麼第二種不可能是一個潛在的金礦，它可以為科學家提供難得的機會，也許是千載難逢的機會，進行變革性發現...

這本書《第二種不可能》與彭羅斯鋪磚大圖有關，也與準水晶有關。這是一個非常有趣的科學發現發掘過程之旅，但是標題完全讓我誤解了，很容易讓人迷惑問什麼是唯一的一種？This book " second kind  of impossible " is related to Penrose's great tiling, and also to the quasi crystal.  it is a very interesting scientific discovery travel, but the title completely make me misunderstood , and it was easy to make confused ask What is the only kind? and I look for all the pictures of Penrose tiling " so I believed the only kind", just one kind, that  consisted of three typpes of decagons,  , the rest are more or less a art-work of the same kind, this really push me to find a different kind of Penrose tiling, In fact , aat about March last year(2022), I already made some different types of Penrose Patterns  with Pentagon shape, and found a coupling technique to extend Penrose tiling, these are  successivelly puall in my Blog,

我找了所有彭羅斯瓷磚的圖片，所以我相信“唯一的一種”由三種十邊形組成，其餘的或多或少都是同類的藝術品，這真的促使我去尋找一種不同的彭羅斯瓷磚，事實上, 大約在去年（2022年）三月份的時候，我已經做了一些不同類型的五邊形Penrose Patterns，並找到了一種耦合技術來擴展Penrose tiling，這些都在我的博客中陸續發布，

You can return  penrose yiles to the original point by turning a 72-degree angle... I have been opinionated looking for   that was different from  the original Penrose tiling  "so defined by myself second kind Penrose tiles"   since the Spring Festival this year (2022).轉個72度角就可以讓彭羅斯回原點了。。。

 I ‧Completely misunderstood Paul Steinhart's original intention  and thought there were lot of second possible accidentially .

從今年春節開始，我就一直在固執地尋找與原來的彭羅斯瓷磚不同的“自己定義的第二種彭羅斯瓷磚”​​

,, -‧完全誤斛Paul steinhart的原意,誤 打誤撞, 自以為 second possible,, 也自行定義了一此作圖規範`然後可以畫出可推衍到無限大的晶胞結構,有五重旋轉對稱性,也有類平移對稱性..我用上化學的簇來命名這種最小的晶胞結構

  如果我有機會寫一本書，我會承認我錯誤地瞭解Paul Steinhart 的書名，而盲目追求自以為是的第二種可能…而意外的找到幾乎所有上百種的正五角形的彭諾斯平鉚圖,, 因為當時, 我不知道自己什麼是對的,,我只是想著會「走出另一種可能」。‧ If I had the opportunity to write a book, I would admit that I misunderstood the title of Paul Steinhart's book, and blindly pursued the self-righteous second possibility...and accidentally found almost all hundreds of regular pentagonal Pennos flat riveting diagrams ,, Because at that time, I didn't know what was right for me, I just thought that I would "go out of another possibility".

如果我有機會寫這本書的話,, 我會引用誤 打誤撞,是會走出另一種可能的. 自以為是的 second  kind possible...就算是對自己未求是甚解, 盲目冒追,,,,進,,  或訐再引用   書中的一句話 「,If one can expose the underlying assumptions and find a long-overlooked loophole, the second kind of impossible is a potential gold mine that can offer a scientist the rare opportunity, perhaps a once-in-a-lifetime opportunity, to make a transformational discovery」如果一個人能夠揭露潛在的假設並找到一個長期被忽視的漏洞，那麼第二種不可能是一個潛在的金礦，它可以為科學家提供難得的機會，也許是千載難逢的機會，進行變革性發現...

 意識到這是一本關於從外太空尋找奇怪的墜落（隕石）石頭的艱苦旅行的書之後，我自己開始環顧所有古董店尋找古老的石頭. .我很幸運的從玩古黃朋友介紹中看到了一塊隕石,這是一件夜間會發出強烈‧綠光的石頭...可惜這位朋友只讓我照局布的圖片.    ,朋友堅持認為稍是一塊與華盛博物館收藏六方金剛石,但是在晚上發光顏色更緣.

定性為六方金剛石,最有名的一顆被收藏華盛頓博物館收藏, 大小約一厘米以上碳90%,鋅鐵鎂等其他物質佔10%,另一顆在中園平民王占奎手上, 關於 Lonsdaleite  定性為六方金剛石‧、學術上的研究己有百年以上的歷史, 尤具是2015年、澳大和亞科學家在實驗室製作出硬度極大的六顆粒類鑽石体.在此根本容不下我來插嘴贅述,,,這類晚上發綠色光的夜明珠在網站上很多,而且價格在台幣伍佰到伍仟元之間都可冒到. 几乎所有的稀世珍品都好像有一個些特別屬於靈性議題的故事,我朋友的夜明珠與大陸平民王占奎手上,的寶物一樣,有一段神化舨情誼故事, 但是這此暫且放下不說,,讓收藏家自述他們的德儀天佑..

我拜訪化的主要的目的就是誚求他準許照二張局布的照片 , ,並且公布在我私人網站, 我相信這塊所謂的隕石確實隱隱約約有五角形狀的表徵,並且在夜間照的綠色圖片明顯的有晶体狀.但是真正的晶体結構分析是需要-X-光照射,以及使用二次離子質譜儀(SIMS)分析材科成分,,可惜, 這個目前很難做到, 因為不知如何保險

 Lonsdaleite is characterized as a hexagonal diamond. The most famous one is collected by the Washington Museum. It is about one centimeter in size and 90% of carbon, 10% of zinc, iron, magnesium and other substances. The other one is in the hands of Wang Zhankui, a commoner in Zhongyuan.ght. Hexagonal diamond‧, academic research has a history of more than 100 years, especially in 2015, UM and sub-scientists produced a six-grain diamond-like body with extremely high hardness in the laboratory. I am not qualified t to intervene here.

    ,,after realizing this is a book of a hard traveling of searching  a strange falling (aerolite)stone from outer space , I  myself  begin  to  look  around all antique store for the old  argurely ugly  stones. . I was lucky to see a meteorite from the introduction of a friend who played ancient yellow. This is a stone that emits a strong ‧green light at night...Unfortunately, this friend only let me take pictures of the layout. ...,,

There are many night pearls that glow green at night on the website, and the price can be found between NT$500 and NT$5,000. Almost all rare treasures seem to have a story that is particularly spiritual. My friend’s collection  Ye Mingzhu is the same as the treasure in the hands of the mainland commoner Wang Zhankui. There is a story of deified friendship, but let’s put it aside for now.

The main purpose of my visit is to ask him for permission to take two photos of the structure and publish them on my private website. I believe that this so-called meteorite does have a faint pentagonal shape and is green at night., but the real crystal structure analysis need tequires X-ray exposure, and SIMS to make material analysis.  It is very difficult  at present to borrow *(bring) this particular stone out without insurance.

Lonsdaleite 

先看看從網路上截錄下關於Penrose 圖的描述(大概是google翻譯的)  .---- 1974年潘洛斯首先定了一条平铺规则："合法”的拼贴必须能使弧线对接，连成连续的曲线 没有这条规则，风筝和飞镖就会摆出重复的图案；而在这条规则之下，就永远都不会出现重复。 风筝和飞镖，永恒地舞动在五条对称轴周围，组合出满天星、十边形，蜿蜒的长线则绘成蝴蝶与花朵的形状。 形态似“似”而非，蕴藏无穷变化。」       關與Penrose tiling「 「阿肯色大学数学系助理教授埃蒙德·哈里斯（Edmund Harriss）的博士论文主题就是彭罗斯贴砖。他为我们做了一个对比：“试想你走在一个由正方形构成的世界里，你每走到一块正方形的边缘，下一块都还是同样的正方形。一直走下去，你都知道会看到什么东西。”而彭罗斯贴砖的性质正好完全相反。“不论你掌握了多少信息、看过多少贴砖排列，你都无法预测下一步的花纹，它将会是你之前从未见过的图案。」He also defined a drawing specification by himself, and then he could draw a unit cell structure that can be deduced to infinity, with five-fold rotational symmetry.

這是一個非常有趣的科學發現旅行，但書名完全被我誤解了，一個退休的懶惰教授只看到書名的, 很容易不由得問唯一種類是什麼？ 這是到底那一種是only kind?? 這到底是我心裡不停問的唯一一種是什麼？ 哪一個是唯一的？？ 應該是最原始的Penrose tiling。把元 轉個72度角就可以回到原點了。。。

從今年（2022年）春節開始，我就一直錯找自以為是和彭羅斯。 到底哪一個是唯一正叉崔的？？ 應該是最原始的Penrose彭羅斯圖。應該就是最正的五重性 Penrose 潘若斯圖,轉72度角可以回到原點…我完全誤斛Paul steinhart的原意,誤 打誤撞, 自以為 second possible,從今年春節 (2022)我就誤打誤撞的去找自以為是最正確的且與 Penrose 不一樣的 second kind 的Penrose 圖 ,,‧我把原始的潘諾斯平鋪圖加了幾個正十邊形變成了正五遑形的彭罪斯圖,( 每邊有五徊十角形) 後來把正五角形彭羅斯圖,每邊減少幾個正十邊形改成了圓形彭羅斯圖 , 廬他們都符合五五重旋轉對稱性, 但是也有類平移對稱性‧我默默的將園放在部落格裡, 寫下了一些註解, 不敢張揚., 因為連我自己都不敢肯之我襖維基百科中間瞭解到的潘洛斯平鋪開圖, 有設有具体更評細的正式的研究文獻解稈說明.  我也陸陸續續的自行定義了一此作圖規範`然後也可以畫出可以有可能推衍到無限大的晶胞結構,有五重旋轉對稱性,也有類平移對稱性.. 一直到去年4月27日, 我到中興大學昆虫系, 給了一個紀念貢校長逝三周年的在中興大學的生活回顧照濱講, 順便講了十幾分鑄的Penrose大圖製作 second kind of impossible ↓當然, 在里暗的演講廳裡, 只能想像化們目然的表情ｏ五日一日, 清華大學校慶, 物理系給我這一個72G畢業校友一個值平校友俊惠, 在自助大餐前, 二十分鍾的演講的機會, 標題也是second kind of impossible, 加上一個我自作的三個不同等邊菱形做的大問號. 我上台後才鶯覺到十年都沒給過比較正式的學術性演講, 在大廳裡, 我看不清會幕上的字, 也看不到紅色的游標指示箭頭. 我相信, 當我斛釋完wiki上面享的彭罪斯鋪碑簡介後, 沒有一個唸過具本幾何的人有信心相信我後面講說的 作圖, 彭羅斯鋪磚圖簡介如下「.二十分鐘只講不到一半, 被飢腸餓肚的物理系友要求只能再講五分鏡, 匆匆的把幾張大圖秀出, 下台一鞠躬,,

 我用上化學的簇來命名這種最小的晶胞結構  ,,如果我有機會寫這本書的話,, 我會引用誤 打誤撞,是會走出另一種可能的. 自以為是的 second  kind possible...就算是對自己未求是甚解, 盲目冒追,,,,進     本書與Penrose 的偉大鋪磚圖有關, 也與quasi crystal 有關. 是一本很有-趣的科學發掘過程  但是書名卻讓我完全誤解,很容易不由得問道•What is the only kind?  這是到底那一種是only kind??應該就是最正的五重性 Penrose 潘若斯圖,轉72度角可以回到原點…從今年春節 (2022)我就誤打誤撞的去找自以為是與 Penrose 不一樣的 second kind 的Penrose 圖,, -‧完全誤斛Paul steinhart的原意,誤 打誤撞, 自以為 second possible,, 也自行定義了一此作圖規範`然後可以畫出可推衍到無限大的晶胞結構,有五重旋轉對稱性,也有類平移對稱性..我用上化學的簇來命名這種最小的晶胞結構  ,,如果我有機會寫這本書的話,, 我會引用誤 打誤撞,是會走出另一種可能的. 自以為是的 second  kind possible...就算是對自己未求是甚解, 盲目冒追,,,,進,,  或訐再引用   書中的一句話 「,If one can expose the underlying assumptions and find a long-overlooked loophole, the second kind of impossible is a potential gold mine that can offer a scientist the rare opportunity, perhaps a once-in-a-lifetime opportunity, to make a transformational discovery」如果一個人能夠揭露潛在的假設並找到一個長期被忽視的漏洞，那麼第二種不可能是一個潛在的金礦，它可以為科學家提供難得的機會，也許是千載難逢的機會，進行變革性發現...