In Class Work

Fractals in Art

Even before mathematicians really studied the algorithms that create fractals, the work of some artists seems oddly fractal in nature. In some cases, perhaps they had a sort of intuitive connection with the mixture of order and chaos in fractals; in others perhaps they actually used a technique similar to the algorithms we use today.

Infinite Regress: The idea of an infinite regress has been around for a long time in art -- an infinite sequence of repeatingly smaller versions of the same image. Here are two relatively modern examples, still done before fractals really were studied extensively or became part of the mainstream:

M.C. Escher, Smaller and Smaller, 1956
The cover of TV Week from the Fresno Bee, date unknown
Early 19th century Japanese woodcuts: Link to a chapter on fractals by Marc Frantz that shows early 19th century Japanese woodcuts side-by-side with amazingly similar computer-generated fractals. (16.1MB)

Jackson Pollock: A physicist/art theorist, in conjunction with another physicist and a computer analyst, feel that they have shown that the drip paintings in Jackson Pollock's paintings are often fractal. By analyzing film of Pollock creating some of his paintings, they decided that the fractals resulted from a systematic construction process involving multiple layers of painted patterns.

They have used the techniques we've learned to calculate the fractal dimension of many of his paintings, and have even studied how the fractal dimension of his works changed over time (it increased over the decade he made his drip paintings, they found). (They have also tried recreating his effects, and did not find that exhibited fractalian behavior -- except when they let the wind blow hanging buckets of paint.)

While there is disagreement among fractal experts as to how mathematically sound this work is, it's still a cool idea.


Jackson Pollock, Autumn Rhythm:Number 30, 1950	Jackson Pollock, Blue Poles: Number 11, 1952
Each layer of paint is, according to the authors of this study, fractal, and each has differing fractal dimension. They have calculated the fractal dimension of the painting as a whole to be D=1.67.	One of Pollock's last drip paintings, now valued at more than $30 million. This was painted over a period of six months, and has the highest fractal dimension of any Pollock painting, as calculated by Richard Taylor -- D=1.72.

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M.C. Escher, Smaller and Smaller, 1956	The cover of TV Week from the Fresno Bee, date unknown