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Did a Chinese calligrapher use ‘fractal expression’?

su.jpg Huai Su’s fractal calligraphy

By Hamish Johnston

In the scientific world, fractals were first identified in the mid-1970s by the mathematican Benoît Mandelbrot.

However, it’s possible that artists and artisans have long been using the fragmented shapes in their work.

In 1999, two Australian physicists famously showed that the “paint-drip” canvasses of Jackson Pollock could be dated by computing their fractal dimension — which tended to increase as Pollock matured as an artist.

Now, Yuelin Li of Argonne National Lab in the US has posted a paper on the arXiv preprint server claiming that calligraphy done by the “maniac Buddist monk” Huai Su more than 1200 years ago contains fractals. Li analysed a request for “bitter bamboo shoots and tea” written by the monk and found that it can be characterized by two different fractal dimensions.

Li believes that the fractal nature of some artworks “can be attributed to the artist’s pursuit of the hidden order of [the] fractal”.

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  1. Alastair Carnegie

    It is certainly possible to detect ‘pathological’ curves in Huai Su’s calligraphy, 1926 Nobel Laureat Jean Perrin wrote:- “The direction of the streight line joining the positions occupied at two instants very close in time is found to vary absolutely irregularly as the time between the two instants is decreased. An unprejudiced observer would therefore conclude that he is dealing with a function without derivative, instead of a curve to which a tangent could be drawn … At certain scales and for certain methods of investigation, many phenomena may be represented by regular continuous functions, If, to go further, we attribute to matter the infinitely granular structure that is the spirit of atomic theory, our power to apply the rigourous mathematical concept of continuity will greatly decrease.”
    Non-differentiable calligraphic trajectories look about ‘par’ for the fractal golf course.

  2. “If the mind is upright, the brush strokes will be right.”
    paola billi xizi

  3. I confess that I fail to see say the self similarity on different scales that one often observes with fractals. However the written description that one of the commenters gave reminds me a bit of what happens when water comes to a boil–a chaotic process.

  4. To Alastair Carnegie
    Very interesting comments. As a physicist I believe in CAUSALITY, not COINCIDENCE. For everthing there is a cause, and there is the effect. What human always tries to do is to make the link between the two at the best of their knowledge and capability.
    In the case of the fractal expression in calligraphy, the effect can be attributed to many different causes or even categorised as coincidence. Yet, as is discussed in the article, the artists were clearly after a group a visuals that can only be unified under the magic of fractal expression.
    To Paola,
    Here is again a beautiful expression of causality:
    Upright mind to upright brush stroke.
    To Null Punk,
    As has been discussed in many papers, real world fractal is diffrent from mathmatically generated fractal patterns. Chaotic is probably the best description for such fractals.


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