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| Jackson Pollock's drip paintings were an important step in the development of modern art, and have been the subject of many analyses in art criticism. Recently, Taylor, Micolich, and Jonas applied the method of box-counting dimensions to look for quantitative differences between these paintings. |
| To study the box-counting dimension of the paintings, they digitized the painting being studied, covered it with a grid of squares of size r, and counted the number N(r) of grid squares that contained part of the drip pattern. |
| Plotting log(N(r)) vs log(1/r), they observed the points fall not along a single straight line, but rather along a broken line. One straight section of the broken line corresponds to r in the range 1mm < r < 5cm, the other straight section to 5cm < r < 2.5 m. |
| The lower range is determined by how the paint drips onto the canvas, the upper range by how Pollock moved across the canvas. |
| Early drip paintings done in 1943 had upper range slopes (the box-counting dimension of the pattern) close to 1. By 1952, this slope had increased to about 1.7. The increase in dimension appears to correlate well with the evolution of Pollock's paint dripping technique. |