Balancing the expected and the surprising in
Bridget Riley’s disc paintings
Neil Dodgson
The disc paintings
Experiment
There is an an æsthetically interesting
range where between a quarter and a
half of a regular pattern is modified.
Bridget Riley produced three disc paintings. My
experimental work was inspired by asking why
she chose particular arrangements of discs as
being, somehow, the “right” arrangements. This
led to my making a range of variations and then
to hypotheses about what is going on.
The experiment refines the hypothesis to two
specific questions: How much of a pattern needs
to be present for it to be immediately obvious to
a human observer? How much of a pattern can
be removed before it ceases to be obvious to a
human observer?
Take a regular arrangement of discs. I suggest:
40
Pattern appearing
D
C
B
A
Normal
35
30
25
Number
Hypothesis
20
15
Removal of 50% or more of the discs leaves
insufficient of the pattern for the brain to spot
any underlying structure to the discs’ arrangement.
Participants were first shown patterns that
gradually appeared over 30 seconds (A–D). They
indicated when the pattern became obvious.
They were then shown patterns that gradually
disappeared over thirty seconds (E–H). They
indicated when the pattern ceased to be obvious.
Removal of less than 25% of the pattern leaves a
“pattern with holes”: the human brain can easily
complete the pattern and we see simply an incomplete version of the whole pattern.
10
5
0
0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Percentage at which pattern becomes obvious
40
White Discs 2 (1964), emulsion on hardboard,
104fl99 mm, the design is a regular pattern from
which 30% of the discs have been removed.
Expected vs surprising
I suggest that the trade-off between the expected
and the surprising operates in two opposing,
complementary, ways: we expect a pattern and
are surprised by the deviation from the pattern;
and, conversely, we expect no pattern and are
surprised by the hints of pattern that emerge on
prolonged viewing.
The cumulative distribution shows that, on the
increasing stimuli, the pattern is obvious in over
80% of cases where 73% of the pattern is visible, and that, on the decreasing stimuli, the pattern is not obvious in 80% of cases where less
than 46% of the pattern is visible. If the pattern
is not known, as is the case if the perturbed
pattern is presented as an artwork, then we need
to consider only the increasing stimuli. This
increases the lower value from 46% to 50%.
This supports the hypothesis that the æsthetically interesting range is between about 50%
and about 75% of the pattern being present.
H
G
F
E
Normal
30
25
Number
Removal of between 25% and 50% of the discs
produces a result which has sufficient structure
for the underlying pattern to be discernible and
sufficient lack of structure for effort to be required to discern that underlying pattern. The
work is thus seen as a work in its own right,
rather than an imperfect version of the pattern.
Pattern disappearing
35
20
15
10
5
0
0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Percentage at which pattern ceases to be obvious
Cumulative distribution
1.00
Proportion of participants to whom
pattern is obvious
There was a significant difference between the
point at which a pattern becomes obvious in the
increasing runs and the point at which a pattern
ceases to be obvious in the decreasing runs. This
indicates that there is a range of values for which
the pattern is not obvious but for which a pattern may still be discerned.
A–D
E–H (+5)
0.80
0.60
0.40
0.20
0.00
0
10
20
30
40
50
60
70
80
90
100
Percentage of pattern visible
When does the pattern become obvious? (A–D)
More complex adjustment
When does the pattern cease to be obvious? (E–H)
Fragment 6/9 (1965), screen-print on plexiglass,
625fl720 mm, limited edition of 75 prints.
This is not created by simple deletion. Assuming
the regular pattern below, we must adjust 43%
of the discs, leaving 57% alone. The adjustments
are: delete disc (9%), insert disc (12%), move
A
A
E
E
B
B
F
F
C
C
G
G
D
D
H
H
100%
90%
80%
pattern is obvious
70%
60%
50%
pattern can be discerned
with some work
40%
30%
20%
pattern is not discernable
Is there more going on?
The art is not just in adjusting a certain
proportion of discs. Riley has also ensured that
her compositions are balanced. The examples at
right show the imbalance that results from using
just a pseudo-random number generator.
“Balancing the expected and the surprising in geometric patterns”, Computers & Graphics 33(4):475–483, August 2009
http://www.cl.cam.ac.uk/~nad10/pubs/CandG09.pdf
doi:10.1016/j.cag.2009.04.001
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