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This motivated scientists from Mexico, Spain and England to study the luminance in Van Gogh's paintings in detail.
促使墨西哥、西班牙和英國的科學家開始研究梵高畫作裡的顏色亮度。
They discovered that there is a distinct pattern of turbulent fluid structures
他們發現梵高畫中有紊流結構，
close to Kolmogorov's equation hidden in many of Van Gogh's paintings.
類似柯爾莫哥洛夫的模型。
The researchers digitized the paintings, and measured how brightness varies between any two pixels.
研究者將這些畫作數位化，并測量兩點像素間的亮度。
From the curves measured for pixel separations,
根據像素間的曲率，
they concluded that paintings from Van Gogh's period of psychotic agitation behave remarkably similar to fluid turbulence.
他們認為梵高精神病期間的作品精準畫出紊流的型態。
His self-portrait with a pipe, from a calmer period in Van Gogh's life, showed no sign of this correspondence.
而平穩期間叼著煙斗的自畫像則不符合紊流的結構。
And neither did other artists' work that seemed equally turbulent at first glance, like Munch's "The Scream."
其他畫家所作類似紊流的畫如孟克的《吶喊》，也不符合。
While it's too easy to say Van Gogh's turbulent genius enabled him to depict turbulence,
雖然我們可以說是梵高的天賦讓他描繪出紊流的結構，
it's also far too difficult to accurately express the rousing beauty of the fact that in a period of intense suffering,
人們很難在承受痛苦時精準表達如此困難的概念，
Van Gogh was somehow able to perceive and represent one of the most supremely difficult concepts nature has ever brought before mankind,
梵高竟然能夠理解并呈現世界上最深奧復雜的概念，甚至早于人類出現的概念，
and to unite his unique mind's eye with the deepest mysteries of movement, fluid and light.
他用獨特的慧眼看透移動、水流和光影的奧秘。
