fractal dimension of abstract art
Roger Bagula
Physics goes abstract
12 October 2005
An image processing technique that is used to analyze galaxies might
also have applications in the world of abstract art. Scientists in the
US and Canada have shown that it might be possible to use
"multi-fractal" analysis to distinguish between works by different
artists (Phys. Rev. E72 046101).
The works of the abstract expressionist painter Jackson Pollock have
already been analyzed with fractal techniques by Richard Taylor of the
University of Oregon and others. This work concentrated on analysing
actual patterns or "blobs" formed by a specific colour on a canvas. Now
Jonas Mureika of Loyola Marymount University in California and
colleagues at the University of Toronto have gone a step further and
analysed the "edges" of these blobs as well.
Figure 1
Figure 1
They looked at over 40 abstract works of art by Pollock (figure 1) and
members of a movement known as Les Automatistes. To analyse the blobs
Mureika and co-workers used digital filtering techniques to isolate
specific colours in the painting (figure 2). To analyze the edges they
used a Sobel gradient filter: basically, areas of high colour contrast,
such as red against green or black against white, appear bright under
this filter, while areas of low colour contrast are dull (figure 3).
Figure 2
Figure 2
They then used a standard "box-counting" technique to determine the
fractal dimension of these filtered patterns. This involves covering a
pattern by a set of squares and counting the number of squares, N, that
contain the pattern. Each box is then divided into four smaller boxes
and the number of boxes that contain the pattern is counted again. This
process is repeated to produce a log-log plot with N on the vertical
axis and the size of the boxes on the horizontal axis. The fractal
dimension is given by the gradient of this graph.
Figure 3
Figure 3
Mureika and co-workers found that the fractal dimension of the blobs
could not distinguish between different artists. However, the edge
technique showed that the fractal dimensions of paintings by Pollock
were statistically significant higher than those by Les Automatistes.
"Since part of the human visual processing system is based on the
detection of such contrast edges, this suggests that there is a
perceptually unique quality about paintings by particular artists," says
Mureika. "It also suggests that edge identification is an important
contribution to 'aesthetic', and might explain why we find one abstract
image more artistically appealing than another, even though we have no
reference point to judge either as 'good' or 'bad'."
The technique could also be used to authenticate works of art and
identify forgeries.
About the author
Belle Dumé is Science Writer on PhysicsWeb