Multifractal structure in nonrepresentational art

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, painted by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific color (“blobs”) and patterns formed by the luminance gradient between adjacent colors (“edges”). It is found that the multifractal analysis method applied to “blobs” cannot distinguish between artists of the same movement, yielding a multifractal spectrum of dimensions between about 1.5 and 1.8. The method can distinguish between different types of images, however, as demonstrated by studying a radically different type of art. The data suggest that the “edge” method can distinguish between artists in the same movement and is proposed to represent a toy model of visual discrimination. A “fractal reconstruction” analysis technique is also applied to the images in order to determine whether or not a specific signature can be extracted which might serve as a type of fingerprint for the movement.

Figure 1

Black-pigment-filtered image P02, $\beta \sim 20$.

Figure 2

Pixel count $N_{\mathrm{px}}$ histogram for black pattern of P04, showing peaks at $(R,G,B)=(21,17,21)$.

Figure 3

Sample log-log (base 10) fits used to determine box and information dimensions for P02, $\beta =20$.

Figure 4

Sample of Les Automatiste painting and black pigment pattern (image A05).

Figure 5

Multifractal dimension spectra for select images of Table . Error bars are suppressed for easy viewing.

Figure 6

Multifractal scaling behavior, showing a one-level reduction of distribution with probilities $r_1,r_2,r_3$, and $r_4$.

Figure 7

Black and white chekerboard pattern (“Hermann grid”) showing visual luminance structure variation due to edge enhancement effects in the visual processing system.

Figure 8

Sample luminace gradients for P02 (top) and A05 (bottom).

Figure 9

$D_q$ spectra for luminance gradients of Pollock, Automatistes, and Avital images $(\beta =1)$. The structures are clearly separated by $D_0$ values, although the overall strucutre of the curve is similar.

Figure 10

Sample luminance gradients of images for AV01 (top) and AV06 (bottom).