Color charts, aesthetics and subjective randomness by ijb17680


									        Color charts, aesthetics and subjective randomness

                                   Yasmine B. Sanderson∗

                                       January 21, 2010


            A statistical analysis of fifty-four “random-looking” art and design color charts
        show that they differ significantly from truly random color charts in the average jump
        between adjacent colors. We argue that this implies that subjective complexity in
        color space is dependent on color distance.

1       Introduction

The color chart, a grid of squares or dots of varying colors, was initially used by artists
for the purpose of studying and classifying color. In 1918-19 members of the Dutch art
movement De Stijl introduced the color chart (and its variations) as artworks in themselves
in its advocation of pure abstraction and use of only the most basic forms and colors [7].
Since that initial introduction, the color chart has been used repeatedly by various artists in
the exploration of many different themes such as randomness, artist control, art as concept
vs. creation. In addition to its presence as art, the color chart has increasingly been used
in design and decoration. Although evidence of its use can be found as early as the 1950’s,
its presence on mugs, posters, beanbags, etc is increasingly common, undoubtedly inspired
by present day’s ubiquitous pixelated color picture screen.

One of the striking similarities in many of these works is that the artist chose to arrange
the colors in a way which one could describe as “random”, as illustrated in this example:
   Emmy-Noether-Zentrum, Department Mathematik, Friedrich-Alexander-Universit¨t Erlangen-
N¨rnberg, Bismarckstraße 1 1/2, 91054 Erlangen, Germany. Email:

                           Figure 1: Happy Pixels by A. Zwierlein

In particular, these arrangements show no obvious patterns or symmetries and are not
likenesses of some person, place or object. We argue that this color chart is an example of
subjective randomness, that is, an example of what people believe randomness should look
like. Studies have established that subjective randomness is quite different from “true” or
stochastic randomness [22] [1] [16]. To illustrate this difference, we show the same color
blocks, arranged by a random generator:

Although it would be difficult to describe exactly why, the first chart looks “more random”
than the second.

In studies involving binary sequences, Falk and Konold [6], and later Griffiths and Tenen-
baum [8] [9], found that those sequences which were rated most random were those who
showed a higher subjective complexity. In particular, these would be sequences which would
be harder to describe, or hold to memory. So XOXOXOXO would be rated as less (subjec-
tively) complex than XOOXOXOO because the first could be succinctly described as “four
times XO”, but the second sequence would have to be described (almost) term by term:
“first an X, then two O’s, then a X,...”. This increased subjective complexity is highly
correlated with a higher-than-normal alternation rate. Studies by Griffiths and Tenenbaum
also find that the presence of certain repetition and mirror symmetries decrease subjective
complexity [8].

In this study we consider 54 “random-looking” color charts found in art and design and
develop a measure which would help distinguish subjectively random color charts from truly
random ones. In comparing the art/design color charts with their random counterparts,
we show that a significant number of these works have non-normal alternation rates (or
average distance) between colors. The situation is extreme for the set of design color charts,
where almost two-thirds had alternation rates higher than 97.5% of their randomly arranged
counterparts. The colored charts which are studied are each unique in their numbers of
blocks, number of different colors and set of colors used. Most of them have few adjacent

blocks with the same color. Therefore, it makes little sense to consider a complexity measure
which simply records changes in color, i.e. “first a yellow, then a white, then an ochre,...”.
Our study gives strong evidence that subjective complexity is dependent on color distance.
We also argue that prevalence of a higher-than-normal alternation rate in design color charts
also indicates its strong aesthetic value and attractivity.

We thank W. Brandt (Hallmark Corp.), B. Drahota (Iso Gmbh), I. Fremer (Remember
Products), M. Kliege (Neues Museum), F. Knop (Erlangen), G. Iverson (UC Irvine), E.
Jost (Thun), G. Martens (Erlangen), R. Scha (IAAA, U Amsterdam [17]), R. Steingrimsson
(UC Irvine), I. Walde (, A. Zwierlein (Sieger Design) for helpful conversations
and information sharing.

2    Experiment

We collected .jpg-files of the images of 26 color chart art works created by a total of 11
artists and 28 color chart design works by a total of 13 designers/design teams. In the
study were all works that we could find which used at least three colors in a grid which
had at least 4 rows and 4 columns of same-sized blocks. We rejected those charts whose
colors were not well defined or which were clearly compositional. For example, we did not
include charts with an obvious global pattern or symmetry (e.g. Ellsworth Kelly’s “Red
Yellow Blue White”, Paul Klee’s “New Harmony”) or for which there was obvious bias in
the arrangement (e.g. graded as color charts used in classifying color. Also see [4] concerning
compositions I-V and VIII of Kelly’s Spectrum series). We also did not include works for
which we knew that a random process had been used to determine the color arrangement
(e.g. Hermann deVries’ “Random Objectivations” [15] or Byron Kim’s “Synecdoche” [14]).
Due to the great number of color charts by Damien Hirst and Gerhard Richter, we studied
only a sample of their works. The files themselves were either donated from the artist or
downloaded from the Internet. A color chart was defined to be “design” if it was used to
decorate a utilitarian object. All other color charts were classified as “art”. Some of the
color charts had pictures in the middle of the color blocks.

                          Figure 2: Picto Red by Ideal Home Range

These foreground pictures were ignored. Only the background color chart was studied.

Using Adobe Photoshop, we then read off the triple of values [L∗ , a∗ , b∗ ] in CIELAB color
space for each colored grid in the image. The color’s lightness is given by L∗ , with white

having L∗ = 100, black having L∗ = 0 and a medium gray having L∗ = 50. The coordinate
a∗ represents the color’s position between red/magenta and green and the coordinate b∗
represents the color’s position between yellow and blue [11]. If the color chart consisted
of M rows and N columns of colors, then the result was a matrix C of color values which
corresponded to the color arrangement in the art work:

                           C = (ci,j )i,j = [L∗ , a∗ , b∗ ]
                                              i,j  i,j i,j        1≤i≤M, 1≤j≤N

We were interested in measuring the alternation, or distance, between two adjacent colors
and used the CIE76 color difference formula, which is simply the Euclidean distance, to
measure it. Although, this formula has been officially superceded by the CIEDE 2000,
certain still unresolved problems (such as discontinuity) with the CIEDE 2000 [19] made us
feel that the CIE76 was the safer choice. The CIE76 distance, or alternation, between two
colors c1 := [L1 , a1 , b1 ], c2 := [L2 , a2 , b2 ] is

                      d(c1 , c2 ) := [(L1 − L2 )2 + (a1 − a2 )2 + (b1 − b2 )2 ]1/2 .

The total alternation Alt(C) for a given color chart C = (ci,j )i,j is then

              Alt(C) :=                    d(ci,j , ci+1,j ) +                    d(ci,j , ci,j+1 ).
                          1≤i≤M −1,1≤j≤N                         1≤i≤M,1≤j≤N −1

and the alternation rate is Alt(C)/(N M − N − M ). For each art/design work, we used
a Monte Carlo simulation and compared its alternation rate to the alternation rates of a
minimum of 10,000 M ×N matrices whose entries were a random permutation (with uniform
distribution) of the the color values {ci,j |1 ≤ i ≤ M, 1 ≤ j ≤ N }. All calculations were
made using MAPLE and R.

3       Summary of Results

Individual results for each painting are given in Tables 2 and 3 at the end of the paper.

An art or design work has supernormal (resp. subnormal) alternation rate if more than
97.5% (resp. less than 2.5%) of the tested randomly arranged charts have alternation rates
less than that of the art/design work. An art or design work has above average (resp. below
average) alternation rate if more than 50% (resp. less than 50%) of the tested randomly
arranged charts have alternation rates less than that of the art/design work. We used a one-
tailed (resp. two-tailed) exact binomial test with a sufficient number of random matrices
in order to obtain 95% confidence intervals contained in non-normal (resp. normal) range1 .
The distribution of color charts among the various ranges is given by the following table.
    In the case of Marquina’s “Dots” and Bartlett’s “Binary Combinations” we were not able to conclude
despite using a sampling of 107 charts. However, our conclusions are the same, independently of how these
two works are classified.

                  Design Color Charts                             Art Color Charts
                          19                   Supernormal               13
                           7                   Above average             9
                           2                   Below average             2
                           0                    Subnormal                3
                          28                       Total                 27

                Table 1: Distribution of color charts according to alternation rate.

The greater variation in alternation rates in the art color charts probably reflects the more
complex and varied nature of creator intention. As opposed to the design charts, which
are intended to be attractive, the art charts are explorations of different themes, including
artist control vs. creation, randomness, and abstraction.

Comment: The CIE Lab color space can also be described with cylindrical coordinates
(L∗ , h, c) where h := arctan(b∗ /a∗ ) gives the hue-angle and c := ((a∗ )2 + (b∗ )2 )1/2 describes
chroma. We tested alternation rates for each isolated variable, but did not obtain results as
clear as in the above experiment. Supernormal alternation rates for chroma were strongly
correlated with supernormal three-variable alternation rates. However, subnormal alterna-
tion rates for lightness were strongly correlated with subnormal three-variable alternation
rates. One could ask whether chroma and lightness play some dual or complementary role
in color perception.

4       Discussion

Previous experiments in subjective randomness of binary sequences usually were of two
types: “production”, in which subjects were asked to create sequences which they consid-
ered to look random, or “judgment”, where subjects were asked to identify or rate objects
based on how likely they would have been produced by a random process. Although this
study of color charts is not a classical controlled experiment, we can still identify most (if
not all) of the color charts as examples of subjective randomness in the sense that they
would be described by a third party as random. In many cases, it is even documented the
artist/designer explicitly and conciously exploring randomness or trying to arrange the col-
ors in a way that looks random2 [4] [10] [21] [23] [24] [3]. What is clear from the results of
our experiment is that these were, for the most part, not stochastically random and there-
fore the overalternation was intentional. Since a high rating of subjective randomness has
been shown to correlate with high subjective complexity [6] [8] [9], and both are correlated
     In two of the artworks showing superalternation, there is no mention of randomness as a motivating
theme. However, from what is known about their motivation or surroundings, one can not help wonder
if there was not a desire to create a controlled disorder such as in subjectively random works. Mondrian
claimed that his “Composition for Checkerboard, Dark Colors” (1919) was inspired by “stars in the sky” [2].
Ray Johnson wrote “I painted Calm Center when I lived across the Hall from John Cage = When he was
writing the Music of Changes.” [12], pieces where chance was used in the composition process.

with a high alternation rate (between O’s and X’s) [5] [22] [18], it is reasonable to expect
that subjective complexity in color space is correlated with color distance.

It should be noted that three of the tested artworks had subnormal alternation rates. As two
of these were coming from artists, George Korsmit [23] and Gerhard Richter [20], exploring
randomness, we cannot simply discount them as the result of some other compositional mo-
tive. We are uncertain as to why their color charts would exhibit extremely low alternation
rates. In previous tests, a minority of subjects rated binary sequences with a lower-than-
normal alternation rate as more random (“positive recency”) [6] [22]. This could be the
analogue for color space, but a conclusive answer needs further investigation.

The nonnormality of many of the color charts, however, cannot be solely attributed to
subjective randomness. First, the superalternation was not restricted to those artists who
were conciously exploring or requiring “randomness”. For example, Eugen Jost dismissed
randomness as a motivation in his arrangements, explaining that he placed colors so that
they would “play against each other” [13]. In addition, the strikingly high rate of superal-
ternating color charts in design works cannot simply be attributed to the designer wanting
to create something random-looking. Since design works are primarily intended to decorate
a commercial and utilitarian object in the hopes of attracting consumers, the (subjectively)
random look must be in some way aesthetically pleasing. We expect that the overalternation
is stimulating and thereby attention-grabbing. However, this would not completely explain
the aesthetic aspect of the overalternation. A consumer will not buy a decorated prod-
uct simply because it has held his/her attention; it must also have a pleasing appearance.
Obviously color choice is a factor in appeal. However, we conjecture that the intense varia-
tion in colors holds its own aesthetic value. If we assume that these superalternating color
charts have high subjective complexity, then it is interesting that designers (and therefore
consumers) are attracted to those designs which have extreme subjective complexity; either
very low subjective complexity (stripes, polka dots, images of flowers, movie stars, etc.) or
those with very high subjective complexity (“random”).

 [1] Maya Bar-Hillel and Willem Wagenaar. The perception of randomness. Adv Appl Math,
     pages 428–454, 1991.
 [2] Carel Blotkamp. Mondrian: The Art of Destruction. Reaktion Books, 2004.
 [3] Wendi Brandt.     personal communication.            Hallmark Gift Wrap Design,
 [4] Jack Cowart. Method and motif: Ellsworth kelly’s ”chance” grids and his development
     of color panel paintings, 1948 - 1951. In Ellsworth Kelly : the years in France, 1948-
     1954. Prestel-Verlag, 1992.
 [5] Ruma Falk. The perception of randomness. In Proceedings of the Fifth International
     Conference for the Psychology of Mathematical Education, pages 222–229, Grenoble,
     France, 1981.

 [6] Ruma Falk and Clifford Konold. Making sense of randomness: Implicit encoding as a
     basis for judgment. Psychol Rev, 104(2):301–318, 1997.
 [7] Tate Online Glossary.
 [8] Thomas Griffith and Joshua Tenenbaum. Probability, algorithmic complexity, and
     subjective randomness. In Proceedings of the 25th Annual Conference of the Cognitive
     Science Society, 2003.
 [9] Thomas Griffith and Joshua Tenenbaum. From algorithmic to subjective randomness.
     In Advances in Neural Information Processing Systems, volume 16, pages 953–960,
[10] Damien Hirst. John, john.,
     1988. audio.
[11] R.W.G Hunt. Measuring Colour. Ellis Horwood Limited, 1991.
[12] Ray Johnson.            Ray johnson mail art (collection              no.   ms   310)., 1951.
[13] Eugene Jost. personal communication.
[14] Byron Kim. Synecdoche.,
     2008. audio.
[15] Andreas Meyer, editor. herman de vries: to be. Cantz Verlag, 1995.
[16] R. Nickerson. The production and perception of randomness. Psychol Rev, 109(2):330
     – 357, 2002.
[17] Institute of Artificial Art.
     source of many .jpg files.
[18] Yasmine B Sanderson. Effective generation of subjectively random binary sequences.
     Adv Appl Math, 43:1 – 11, 2009.
[19] Guarav Sharma, Wencheng Wu, and Edul N. Dalal. The ciede2000 color-difference
     formula: Implementation notew, supplementary test data, and mathematical observa-
     tions. Color Research and Application, 30(1):21 – 30, 2005.
[20] Robert Storr. Gerhard Richter : forty years of painting. Museum of Modern Art, 2002.
[21] Robert Storr. Gerhard Richter : doubt and belief in painting. Museum of Modern Art,
[22] Willem Wagenaar. Generation of random sequences by human subjects: A critical
     survey of literature. Psychol Bull, 77(1):65 – 72, 1972.
[24] Andreas Zwierlein. personal communication. Sieger Design for Sitting Bull GmBH,

Table 2: Design Color Charts: The right hand column gives the percent of random color
charts whose alternation rate was less than that of the indicated design color chart.
 Chart    Designer/ Manufacturer     Object               Name                 M ×N      Percentile

          Andreas Zwierlein          Beanbag fabric       Happy Pixels         12 × 34      > 99.99

          Ingo Walde                 Poster background    Paisley              8 × 10       > 99.99

          Nina Marquina              Area rug             Quadros red          12 × 8       > 99.99

          Ideal Home Range           Paper napkins        Flip blue             5×5         > 99.99

          Ideal Home Range           Paper napkins        Flip red              5×5         > 99.99

          Fremer Design              Mug                  Mosaic               13 × 13      > 99.99

          Alexander Girard           Upholstery fabric    Quatrefoil silver     8×9           99.94

          Ideal Home Range           Paper napkins        Picto blue            7×7           99.86

          Nina Marquina              Area rug             Quadros blue         12 × 8         99.84

          Alexander Girard           Upholstery fabric    Quatrefoil emerald    8×9           99.84

          MiquelRius                 Stationary           Mosaic               10 × 8         99.84

          Ideal Home Range           Paper napkins        Picto red             7×7           99.84

          Alexander Girard           Upholstery fabric    Quatrefoil violet     8×9           99.81

          Ideal Home Range           Paper napkins        Flip brown            5×5           99.81

          Stewo                      Paper products       Boas                  5×5           98.99

          Kracht GmbH                Kitchen towel        Kaffee Cappucino       5×4           98.93

          Ideal Home Range           Paper napkins        Picto brown           7×7           98.80

          Fremer Design              Breadboard           Mosaic               13 × 21        98.35

          Nina Marquina              Area rug             Dots                  5×6           97.60

          Ideal Home Range           Paper napkins        Fall squares          4×4           94.00

          Wendi Brandt               Wrapping paper       Kids’ Dot             7×6           86.31
          ˚sa Grey
          A                          Area rug             Uldum                 4×4           80.16

          Stride Rite                Gift certificate      unknown               5×8           75.36

          Fremer Design              Breadboard (small)   Mosaic                4×6           74.22

          Fremer Design              Breadboard (large)   Mosaic                4×6           69.20

          Fremer Design              Napkins              Mosaic               10 × 10        62.55

          Kracht GmbH                Kitchen towel        Eisstern              4×4           24.16

          Jackie Shapiro             Notebook             Multidot              5×4           16.27

Table 3: Art Color Charts: The right hand column gives the percent of random color charts
whose alternation rate was less than that of the indicated art color chart.
 Chart     Artist                   Title                                            M ×N      Percentile

           Eugen Jost               untitled (2009)                                  10 × 10      > 99.99

           Eugen Jost               3.14159... (2008)                                17 × 17      > 99.99

           Damien Hirst             Ellipticine (2007)                               9 × 12       > 99.99

           Ellsworth Kelly          Spectrum of Colors VI(1951)                      38 × 38      > 99.99

           Damien Hirst             Flumequine (2007)                                9 × 12         99.81

           Damien Hirst             LSD (2000)                                       9 × 12         99.78

           Paul Klee                Farbtafel (1930)                                  5×7           99.75

           Ray Johnson              excerpt from Calm Center (1951)                  16 × 16        97.70

           Piet Mondrian            Checkerboard (Dark Colors)(1919)                 16 × 16        99.53

           Damien Hirst             Opium (Unique Version) (2000)                    9 × 12         99.49

           Damien Hirst             JohnJohn (2009) (left panel)                     10 × 11        99.38

           Ellsworth Kelly          Colors for a Large Wall (1951)                    8×8           99.30

           Eugen Jost               Zeichen und Zahlen (2008)                        11 × 11        99.29

           Damien Hirst             JohnJohn (2009) (right panel)                    10 × 11        96.96

           Jim Dine                 The Studio (Red Devil Color Chart No.1) (1963)    6×4           93.42

           Gerhard Richter          256 Farben (1974)                                16 × 16        92.97

           Damien Hirst             Doxylamine (2007)                                9 × 12         89.43

           Ellsworth Kelly          Spectrum of Colors VII (1951)                    40 × 40        81.08

           Georges Vantongerloo     ´
                                    Etude (1918)                                      6×7           66.78

           Gerhard Richter          180 Farben (nr. 300-1) (1971)                    15 × 12        64.73

           Ellsworth Kelly          Sanary (1952)                                     6×7           63.99

           Gerhard Richter          192 Farben (1966)                                16 × 12        59.88

           George Korsmit           2ndcolourhealingscreen (chance) (1999)           24 × 34        17.94

           Jennifer Bartlett        Binary Combinations (1971)                        5×6            2.50

           George Korsmit           1stcolourhealingscreen (chance) (1999)           27 × 21         1.05

           Gerhard Richter          1025 Farben nr. 357-2 (1974)                     41 × 25         0.06

           Piet Mondrian            Checkerboard (Light Colors)(1919)                16 × 16         0.04


To top