Supplementary Information
1. Supplementary Methods
Here we provide (1) tips for the perception of DMP, (2) a brief experiment which demonstrate basic
characteristics (Experiment I; Fig. 1b), (3) supplementary notes for experimental design of intersecting
angles (Experiment II; Fig. 2), subjective rating (Experiment III; Fig. 3b), and orientation shift
measurement (Experiment IV; Fig. 3c). For all experiments reported in this paper, the stimulus order in
each session was adequately randomized. In Exp. III and IV, as obvious in the main text, the color of
repetitive patterns or extrinsic DVNs was set to red to allow for better discrimination between them.
Tips for the perception of DMP
(1) For monocular viewing (a pattern vs. intrinsic DVN), occluding one of your open eyes
with your palm would be better than closing the eye.
(2) Fix your eye on the pattern. You can smoothly move your eye a little bit, but avoid
saccadic eye movement.
(3) You may prefer the repetitive pattern to be with low luminance (i.e., printed on a piece of
a paper).
(4) For the first attempt, it may take several tens of seconds for the onset of the dominance of
closed eye.
(5) It is better to avoid fixating your eye to areas where the repetitive patterns are not smooth
(The center of the spirals, for example).
(6) As described in the paper, the perceptual dominance of the vision of the opened eye
(“pattern” side) and that of the closed eye (“noise” side) changes spatio-temporally.
Therefore you have to be very careful to catch the onset of DMP and concentrate on the
spatial structure. It disappears in few seconds.
(7) While the pattern to the opened eye is perceived, you may notice very weak impression
of the vision of closed eye which is noisy and shimmering. Just keep your attention to
the impression, and then the clear onset of the dominance of closed eye would
gradually or suddenly occur.
Experiment I. Basic characteristics
The characteristics of the mesh pattern that we report in the paper with Fig. 1b are obvious once it is
perceived. They can be summarized in one sentence; irrespective of the noise kinds, the geometrical
structure of apparent mesh pattern in dominant noise is “diagonally” transferred from the suppressed
1
pattern. Here, instead of explaining each combination shown in Fig. 1b, we describe a simple experiment
to briefly confirm this diagonality and its independence on the noise kind. Four participants who gave
affirmative responses for both with intrinsic and extrinsic DVNs in preliminary observations were
recruited. At this point, they were only asked whether they perceived mesh-like structure when intrinsic
or extrinsic DVNs are dominantly seen. These four participants were naive to the purpose of the
experiments; they were not informed of the diagonality of orientation in advance. None of the authors
participated in this experiment.
Several repetitive patterns were presented under dichoptic viewing with the extrinsic DVN (same as
that described in Fig. 2). Then, the dominance of noise occasionally occurs. Participants were asked to
choose one of the PC-generated mesh patterns that were shown in advance (Supplementary Fig. 1) as the
one with the most similar global structure. The variations of 12 candidate mesh patterns are shown in Fig.
1 (i.e., with various rotations, shifted position, etc). Each repetitive pattern has a corresponding candidate
mesh pattern in terms of 45° intersection angle. However, as shown in Fig. 2, the apparent intersecting
angle varies from 30° to 45° and the candidates rarely precisely coincide with an apparent mesh pattern.
Supplementary Figure 1 | Verification. Vertically piled sine curves with four rotations
as test figures (top), and mesh patterns as candidates (bottom).
The reason for fixing the angle at 45° is to reduce the number of candidates and to briefly verify the
basic characteristics. Participants were also asked to report several aspects of their perception (e.g., the
certainty factor, and the detailed orientation and direction of the pattern by free sketching if possible).
The results will be reported in future papers. Here, let us just focus on Fig. 1b3 variations (vertically
piled sine curves, or sinusoidally modulated gratings with various rotations; enlarged images in
Supplementary Fig. 1). These patterns are too complicated to guess the corresponding “diagonal” mesh
patterns and thus, if participants could successfully combine these patterns with the corresponding mesh
2
patterns, the diagonality would be validated. The overall rate of combining patterns in terms of
diagonality is 81% (13/16). The same participants also participated in another session after a sufficient
rest interval. The same experimental settings were applied, except intrinsic DVN (i.e., monocular
condition) was used instead of extrinsic DVN. The overall rate is 100%. Whether the noise is intrinsic or
extrinsic does not affect the global structure of mesh pattern. This result briefly demonstrates the
texture-independent diagonality, because textures of intrinsic and extrinsic DVNs are significantly
different. Note that none of the participants noticed the “diagonality” of the mesh orientation until they
were informed after the experiments.
Experiment II. Intersecting angle
Here we describe several notes with the psychophysical experiment about the intersecting angle
between stripes and DMPs.
(1) The extrinsic DVN used in the experiment (the detail is described in the legend of Fig. 2) is
sufficiently denser than that by a detuned TV monitor with a normal viewing distance. The reason is that
the latter DVN is too coarse to evoke smooth DMP.
(2) Although the adjuster was presented simultaneously with the stripes and the extrinsic DVN, it
was almost always visible, because it broke the redundancy of the stripes. Binocular rivalry has the
tendency that areas with higher visual information win against the other2.
(3) To determine whether there is any anisotropy of saliency of DMP perception, subjects were asked
to rate the saliency using a scale in which DMP perception with horizontal stripes was rated 5 (which
was presented beforehand) and no DMP perception was rated 0 (data not shown).
Experiment III. Subjective rating
Here we describe how the intensity of DMP is defined and assessed with respect to the degree of
randomness in visual noise in the experiment. The regular grid of dots (w=0), when presented alone (i.e.,
no radial bars to the other eye), evokes spontaneous perceptual grouping along horizontal (or vertical)
orientation. The dichoptic viewing of random dots (w=0.6) and the radial bars strongly
evokes the grouping underlying the corresponding DMP. A horizontal Glass pattern (w>0, the
perturbation is applied to each horizontally aligned pair) evokes either or both horizontal grouping or
that of DMP. In other words, a horizontal Glass pattern induces the mixed perception of the two different
groupings. As w varies, the proportion of the mixture changes. The intensity of DMP is defined as this
proportion, since it is subjectively measurable.
The intensity of DMP with dichoptic viewing of random dots (w=0.6) and radial bars was set to 10
(where intensity 0 indicates no DMP perception). As the instruction to participants, the orientation of
perceptually and spontaneously grouped lines was stressed as the relevant feature to judge. Subjects
were asked to rate the intensity of DMP, viewing horizontal Glass patterns with various w and the radial
3
bars dichoptically. Random dots (w=0) were presented to subjects every time they needed them for
comparison.
The transition from orientation illusion to DMP revealed in this experiment is obvious when
Supplementary Fig. 2 is viewed dichoptically with radial bars. When you try it by yourself, adjust the
viewing distance properly. Then you may notice that apparently curved dotted lines in the grid of dots
and the lines in DMP smoothly transit from left to right.
Supplementary Figure 2 | Continuity of orientation illusion and DMP. Here the grid
of dots (w=0 at the left end.) gradually shifts to a horizontal Glass pattern (w=0.6 at the
right end). The close relation between orientation illusion and DMP is obvious when this
figure is dichoptically viewed with radial bars.
Experiment IV. Orientation shift
We used the PEST procedure, first devised by Taylor and Creelman29, and for the measurement of
orientation illusion we applied a simplified version of PEST introduced by Wade and Wenderoth28. In the
binocular condition, a test figure was created by the superimposition of two images; horizontal stripe and
a regular grid of dots described in the paper (w = 0). The grids of dots were rotated with angles θ = 15°,
30°, 45°, 60°, 75°. Therefore the total number of dot patterns was 5. In each trial, a test figure and the
target figure (initially rotated 16° counter-clockwise from the orientation of the grid of dots so the test
figure has a larger slope) were alternatively presented for 5 sec each with an inter-stimulus interval (ISI)
of 1 sec. Subjects were asked which slope is larger, that of the grid of dots or the line segments in the test
figure. Following the subject’s response, the test figure was rotated with the determined rotating step size
so as to decrease the difference of slope. Every time the response reversed, the step size got smaller. One
4
trial continues until the next step would be 0.25°. In the dichoptic condition, red stripes are presented to
the left eye, while the grid of dots and the target figure was presented to the right eye. The rest of the
procedure was the as same as in the binocular condition. The amount of shift was set as 0° at θ = 0° and
90° without the measurement with these angles, because basically the shift can not occur at these
rotational angles in this experimental setting.
Supplementary Figure 3 | Sequence of stimuli. Binocular condition (left) and dichoptic
condition (right).
3. Supplementary Discussion
Similar Phenomena
Here we list three phenomena that seem closely related to DMP: Complementary Image,
Complementary afterimage8-10,30,31 (Supplementary Fig. 4) and the Enigma figure7,11,32 (Supplementary
Fig. 5). Details are given in the legends.
Let us consider why DMP is so spatially clear compared to these phenomena. In the latter, such as
MacKay’s complementary images and Enigma, trade-off relations exist between the intensity (degree of
clearness) and area size of noise flow, meaning that inevitablely the spatial component of the flow is
difficult to examine. By contrast, DMP involves exclusive perception of noise under the interocular
influence of simultaneously presented repetitive patterns. This breaks the trade-off and enables
examination of the spatial component of the flow.
5
Supplementary Figure 4 | MacKay’s Complementary image and afterimage. Over
noise areas in the left figure, the “rose” impression as shown in the right figure can be
evoked. When the visual noise between the black bars is dynamic, the impression is
more salient, and also a rotating motion is perceived (complementary image). After
keeping the eyes focused on the radial bars, quickly shifting the eyes to a blank field
evokes rotating noisy flow perception (complementary afterimage (CAI)).
Supplementary Figure 5 | ”Enigma”-like figure “visual phantom” version (courtesy
of Akiyoshi Kitaoka). Noisy flow with shimmering texture is salient over gray uniform
bands (left). Spatial impression of the flow is simulated (right). In the simulation, DMP for
radial bars are simply blurred and limited on the narrow bands. Similarity between the
right image and the apparent perception evoked by the left image strongly suggests that
the shimmering texture of the flow is a limitative perception of DMP with intrinsic DVN.
The boundary between the radial bars and the gray uniform bands in this visual phantom
version is blurred. When monocularly viewed, this kind of Enigma figure occasionally
evokes smooth perceptual shift from the apparent noisy flow along the bands to intrinsic
DVN and thus DMP by radial bars (i.e., the bottom of Fig. 1b2).
6
Model
Let us summarize the notion presented in the paper and add some notes. We hypothesize that there
exists mutual lateral interaction between visual noise (or ongoing oriented activity) and stimulus-driven
oriented activity. “Mutual” interaction in this paper is defined as two distinct activities maintain their
identities through continuous interaction; “noise” remains noise, and “pattern” remains pattern. For
example, if one activity is absorbed by the other, it is not regarded as mutual interaction. Such mutual
interaction between noise and stimulus-driven activity in brain has not been demonstrated yet, and
DMP could be the first evidence of this.
In the paper we point out the possibility that the stable balanced orientations of interaction could be
reflected (or printed) on the visual noise, resulting in an apparent mesh pattern, providing that the
interaction was effectively and recurrently feed-backed. In psychophysics, the interaction is measured
as the amount of apparent orientation shift in orientation illusions. When the amount of apparent shift is
measured under a certain condition, we obtain for example the data shown in Fig. 3c. As for Fig. 3c, 0°,
90° and the diagonal angle crossing the abscissa in the figure (~45° for convenience’s sake, hereafter)
indicate balanced orientation where shift does not occur. When it comes to “stably” balanced
orientation, it is equivalent to the stable equilibrium point (SEP), a term used in dynamic systems,
regarding the interpolated curve of Fig. 3c (Supplementary Fig. 6a) as a return map (Supplementary Fig.
6b). Thus ~45° is the SEP of the map. On the other hand, at 0° and 90°, even slightest perturbation
breaks the equilibrium state (i.e., unstable equilibrium point; UEP). Note that at least one SEP exists for
any orientation interaction, taking the symmetry of vision into account. According to our notion, the
structure of a mesh pattern depends on the orientation shift map. Three types of orientation shift maps
and the corresponding structures of mesh patterns are illustrated in Supplementary Fig. 6c. Left figures
are typical graphs obtained by previous studies. In c1, as the real angle expands, the shift changes from
expansion to contraction20. Figure 3c is categorized as this type. In the case of expansion only (c2)18,21,
SEP is ~90° and UEP is ~0°. c3 shows the same expansion and contraction as c1, but with the reverse
order18. In c3, two SEPs exist at ~0° and ~90°; one UEP is at the intersecting point between the map
and the abscissa axis, which is in most cases less than 15°. The contraction in this case represents the
illusional amount of Frazer illusion. According to our idea, the interaction underlying DMP are required
to be c1 type. We examined the stimulus combination which evokes orientation illusion, finding a close
similarity to the combination for DMP (Fig. 3c). As the result, we get c1 type, as we would expect.
7
Supplementary Figure 6 | DMP as a stable equilibrium point of orientation
interaction. a, An interpolation curve (f) is added to Fig.3c. b, Suppose that the
orientation shift occurs recursively, then the curve can be regarded as a return map (θt+1
= f(θt)+ θt where θt is the angle θ at time step t) which has one or more stable equilibrium
points (SEPs). c, Three typical orientation shift maps obtained in previous studies (left)
and the corresponding hypothetical mesh patterns (left) with radial bars as the repetitive
pattern (c1, c2 and c3). Expansion and contraction (c1). Expansion only (c2), and
expansion and contraction as in a, but with the reverse order (c3). SEPs are indicated by
a green circle, and UEPs with a red circle.
4. Supplemental Notes
29.
Taylor, M. M. & Creelman, C. D. PEST: Efficient Estimates on Probability Functions.
The Journal of the Acoustical Society of America 41, 782-787 (1967).
30.
Georgeson, M. Antagonism between channels for pattern and movement in human
vision. Nature 259, 413-415 (1976).
31.
Gregory, R. L. A comment: Mackay Rays shimmer due to accommodation changes. Proc
Biol Sci 253, 123 (1993).
32.
Zeki, S. The cortical Enigma: a reply to Professor Gregory. Proc Biol Sci 257, 243-245
(1994).
8