Hallucinations can occur in both healthy and unwell people. Drugs, sleep deprivation, loss of vision, and migraines can all trigger visual hallucinations in people with no psychiatric illness. We have known for more than 200 years that flickering light can induce hallucinations in almost anyone. However, the unpredictability, complexity and personal nature of hallucinations make them difficult to measure scientifically, and previous studies often had to rely on drawings and verbal descriptions.

Pearson et al. now show how to induce visual hallucinations in anyone , and how to measure them objectively and reliably without relying on subjective reports or drawings. The participant volunteers were university students with no history of migraines or psychiatric disorders. The students watched an image of a plain white ring flicker on and off around 10 times per second against a black background. All individuals reported seeing pale grey blobs appear in the ring and rotate around it, first in one direction and then the other. These grey hallucinations are much simpler than the complex multi-shape hallucinations people generally experience and so they are easier to study objectively.

To measure the hallucinations, Pearson et al. placed a second ring marked with permanent perceptual grey blobs inside the white ring. By stating whether the hallucinated blobs were lighter or darker than the real blobs, the participants were able to communicate the strength of their hallucinations. Similarly, by indicating when the hallucinated blobs had moved past fixed lines at the top and bottom of the white ring, the subjects were able to convey the speed of the hallucinated motion.

The hallucinated blobs and ‘real’ perceived blobs had many of the same properties, and seemed to arise in the same part of the brain, the visual cortex. By using the data to construct a neural computer model of visual cortex, Pearson et al. propose a mechanism that can explain both normal vision and hallucinations. The next step is to investigate whether the experimental methods can also model the hallucinations produced by psychiatric disorders.

Hallucinations occur across a wide range of pathologies and are also common in non-clinical populations (Barrett, 1993; 1994). Generally, hallucinations are defined as an involuntary percept-like experience in the absence of an appropriate direct stimulus (Bentall, 1990). However, very little is known about the mechanisms underlying hallucinations, due largely to the methodological constraints caused by their inherently subjective, constantly changing heterogeneous content.

Visual hallucinations are thought to arise in exceptional circumstances when external stimuli are overwhelmed by internally generated spontaneous patterns of neural activity. This situation occurs when the parameters governing normal visual function are altered due to changes in brain anatomy or physiology (Ffytche, 2008; Butler et al., 2012), state changes such as dreaming or migraines (Llinás and Ribary, 1993; Aurora and Wilkinson, 2007), psychotropic drugs that temporarily perturb normal cortical function, or empty full field luminance flicker (Passie et al., 2008; Billock and Tsou, 2012). However, across these classes of hallucination, understanding has been severely limited by the multi-feature (color, form and motion) heterogeneous content that changes unpredictably over time, and typically requires subjective reports or subsequent depiction such as drawing to communicate subjective experience (Allefeld et al., 2011). To study visual hallucinations, we constrained empty-field flicker to a thin annulus that was centred on the fovea (Figure 1A) . This stimulus effectively constrained the hallucinated forms to one spatial dimension.

Figure 1

Download asset Open asset

When a white annulus was flickered on/off on a black background (~2–30 Hz), we noticed that light grey blobs appeared and rotated around the annulus, first in one direction then the other (Figure 1A; see Videos 1 and 2). Unlike full field luminance flicker stimulation whose content changes as a function of flicker frequency (Allefeld et al., 2011; Mauro et al., 2015), the light grey blobs remained clearly observable across the range of oscillation frequencies tested. This reduces the visual feature dimensions and overcomes many of the prior limitations set by the multi-feature heterogeneous content in pathological, spontaneous and full field flicker induced hallucinations.

Video 1

Download asset

Video 2

Download asset

To measure the strength of this hallucination, we devised a technique allowing us to assess the effective contrast with a two alternative forced choice procedure. We presented an interior annulus housing physical sinusoidal luminance modulation simultaneously with the flickering annulus (Figure 1B). We presented this physical retina-sourced annulus at a range of different contrasts and participants reported whether it was higher or lower in contrast than any content in the flickering empty annulus. Across two experiments, data from 28 and 24 subjects were fit with cumulative Gaussian functions to give an estimate of the point of subjective contrast equivalence. This gave us a proxy of the effective contrast of the hallucinated blob structures across different flicker frequencies. Figure 1D shows the effective contrast of the hallucinations as a function of flicker frequency. Contrast estimates peaked around 11 Hz, then continued to decline slowly as a function of frequency (main effect frequency: exp. 1A F(3,81) = 3.42, p=0.021; exp. 1B: F(3,69) = 5.81, p=0.001).

One proposition is that flicker induced hallucinations might be largely due to an interaction between perception and retinal after effects (Bidwell, 1897). To test for a cortical contribution to the hallucinated blobs, we devised a version of the hallucination-contrast experiment that depended on cortical interocular cross-talk. We presented two small annuli, one to each eye using a mirror stereoscope, and flickered both rings either synchronously or asynchronously at 2.5 Hz to 20 new participants. In the asynchronous condition binocular neurons should receive flicker stimulation at ~5 Hz (rather than 2.5 Hz). Accordingly, if the hallucinated content is the product of binocular neurons, viewers should experience higher contrast in the asynchronous condition as 5 Hz is closer to the 11 Hz peak in contrast, we found in the first experiment. Figure 1E shows exactly this; hallucinations in the asynchronous 2.5 Hz condition were perceived at a higher contrast than in the synchronous condition (t(19) = 2.60, p=0.018). Likewise, the same experiment performed at 21 Hz yielded the opposite pattern of results, the synchronous condition gave higher contrast values (t(19) = 2.28, p=0.034; interaction: F(1, 19) = 8.06, p=0.011), as hallucinations produced by >21 Hz flicker were perceived as lower in contrast in our first experiment (Figure 1D). Together these data suggest that flicker induced hallucinations transpire at or beyond binocular neurons and cannot be the sole product of retinal afterimages.

To measure the motion dynamics of rotation in this hallucination, we devised a technique allowing us to quantify the speed of rotation similar to that used in (Wilson et al., 2001). Observers depressed and held a key when a monitored section of the rotating hallucinatory pattern passed a nonius line at the top of the annulus (Figure 1C). Observers then released the key only when the monitored section of the pattern reached a bottom nonius line, marking a travelled distance of half a rotation. This technique gave us propagation times for a fixed annulus distance, hence the speed of the travelling hallucination. The rotational speed was dependent on the annulus flicker rate (Figure 1F), with higher frequencies giving faster rotation speeds (F(2,10) = 24.75, p<0.001).

To learn how rotation speed varies with eccentricity, we scaled our entire stimulus across three different mean annular radii and using the same timing procedure mapped speed in 6 observers. Using the same speed procedure as above, the mean speed for eccentricities of 6.19°, 7.96°, and 9.67° (mean radii) were 34, 33 and 33° s⁻¹. Based on the hypothesis that the hallucinated structure and motion originates in primary visual cortex we converted visual distance into physical distance on the cortex in cm using the detailed surface map of human V1 (Horton and Hoyt, 1991). Figure 1G shows longer propagation times as a function of greater neural distance, corresponding to a mean propagation speed of 5.6 cm s⁻¹ over V1 surface.

Next we tested whether the hallucinations could propagate across gaps in the flickering annulus stimulus. We added 4, 8, and 12 permanent gaps (0.59° width) into the flickering annulus at cardinal locations and sub-cardinal divisions (Figure 1H). Eight observers monitored the direction of motion of the hallucinated blobs by holding one of the designated keys down or reported no clear direction by releasing keys for multiple 60-second durations. Figure 1H shows the percentage of time observers reported rotational motion vs. stationary patterns as a function of gap number. There was a clear trend of less rotation with a greater number of gaps (F(2,6) = 14.68, p=0.005). Next we held the number of gaps constant at four, and manipulated gap size across three different values (0.59°, 1.78°, 2.97°), while observers again tracked hallucinatory motion or its absence. Again, the percentage of time rotational motion was perceived went down as a function of gap size (F(2,6) = 15.93, p=0.004) (Figure 1I).

To learn if these hallucinations are specific to luminance flicker or generalize to isoluminant color flicker, we ran a new experiment with five observers who tracked static shapes, moving shapes, or no structure at all, for both the standard luminance flicker and subjective isoluminant red and green annuli. We first assessed subjective isoluminance in each observer using the flicker fusion technique (Wagner and Boynton, 1972). Using these color values we flickered annuli at 6 or 12 Hz for 30 s. Figure 1J shows the percentage of time reported for each category (no shape, shape only, and shape + motion) for luminance and isoluminance stimuli collapsed across flicker frequency (main effect and all interactions for flicker frequency: all ps > 0.29). Strikingly, unlike luminance stimuli, observers reported no pattern for over 60% of the time at isoluminance (F(2,8) = 39.67, p<0.001). These data suggest a neural locus sensitive to luminance, but not color flicker, likely the dorsal visual processing stream, which has a higher proportion of cells blind to isoluminance (Shapley, 1990). However, we only tested isoluminant red/green, so it remains unknown if this pattern would extend to blue/yellow stimuli.

Over the past several decades researchers have been fascinated by perceptual bistability as a method to study the neural correlates of consciousness and how the brain makes decisions (Blake and Logothetis, 2002). Accordingly, we wondered if the motion in this hallucination might indeed be bistable and hence open a new window into the study of how the brain makes choices for conscious experience. First, to investigate if people hallucinated clockwise and counter-clockwise motion equal proportions of time, 9 observers tracked rotation direction for 10 min. Figure 2A shows equivalent percentages of time reported for each motion direction (CW vs CCW: t(8) < 1, p=0.53). One classic hallmark of bistability is that the distribution of dominance durations exhibit a long tail (occasional long durations), forming a gamma-like distribution (Blake and Logothetis, 2002). Figure 2B shows a clear long tail for dominance durations for the hallucinated bistability, consistent with the core characteristic of other bistable perceptual phenomena.

Figure 2

Download asset Open asset

To obtain more objective performance based measures of this rotational bistability we tested whether sensitivity to retina-sourced physical motion stimuli presented within the annulus might differ when presented congruently or incongruently with the hallucinated motion. This would demonstrate an interaction between hallucinated content and physical discrimination – supporting a common mechanism. A new set of 10 participants tracked hallucinated motion alternations for periods of 10 s. At a random time-point during the final 5 s of tracking a physical motion probe (Figure 2C; see Materials and methods) was presented in the annulus at either left or right of fixation and participants had to report on which side the probe was presented (a two alternative forced choice task). The probe was presented at one of six different contrasts (9.5%, 10%, 11%, 13%, 17%, 25%), set during pilot tests. Probe data was then separated based on probe direction, congruent or incongruent with the concurrent hallucination direction, and probe accuracy was fit with a non-linear function to give a threshold estimate of 70% accuracy (see Materials and methods). Figure 2D shows a significant difference between mean contrast thresholds for congruent and incongruent trials, with greater sensitivity to the probe stimulus when it was rotating in a congruent direction with the hallucinatory percept (t(9) = 2.8, p=0.02). This suggests that the hallucinatory motion percept (or tracking it) weakly suppresses or boosts retina-based motion depending on the motion congruity.

Next we wondered if hallucinated bistability, like perceptual retina-sourced bistability such as binocular rivalry, undergoes a local form of adaptation resulting in longer dominance durations over time (Suzuki and Grabowecky, 2007). For example, binocular rivalry alternations slow during viewing or when the stimulus is moved through visual space (Blake et al., 2003). Participants continuously tracked hallucinated alternations for a 5-min period in a small annulus, immediately followed by a further 5 min of tracking in a larger annulus, that did not spatially overlap with the prior stimulus (order was counter-balanced). Figure 2E shows that dominance durations increased over time during a session of same-sized stimulus. Further, in the second period of hallucination tracking, the new different-sized and non-overlapping annulus did not ‘follow on’ from the slower dynamics, but returned to the original shorter durations. These data suggest that hallucinated bistability can undergo a form of sensory adaptation that is local in visual space. To test if these changes in alternation rate were due to adaptation to the hallucinated content or due to adaptation to the actual perceptual flicker, six participants tracked alternations for 10 consecutive 30 s periods at three different flicker rates (8.5, 10.6 and 14.2 Hz). Figure 2F again shows adaptation, with an increase in dominance durations over time, however across the whole period the alternation rate was not statistically different between the three flicker rates (F(2,24) = 1.76, p=0.19), suggesting the change in alternation rate was not due to flicker adaptation, but most probably due to neural fatigue in neurons representing the hallucinatory bistable structure.

Another hallmark of perceptual bistability is the striking stabilization of the normal continuous stochastic dynamics by a sensory memory between intermittent presentations (Pearson and Brascamp, 2008). To learn if these bistable hallucinations show a similar sensory memory we presented the flickering annulus to eight participants for 2 s followed by 4 s without flicker (repeating intermittent presentation). Participants reported the dominant rotation direction on each 2 s presentation for 100 trials. Figure 2G shows the hallucination motion stability as the percentage of reported motion direction consecutively the same (e.g. clockwise, clockwise), such that reporting the same percept on every trial would result in 100% stability (Pearson and Brascamp, 2008). All individual subjects show a stability measure above the chance score of 50% (two rotation directions), with the mean significantly above chance (75%; compared to 50%: p<0.001), suggesting that hallucinated bistability can be stabilized by a novel form of memory across intermittent presentations.

Finally, to probe for potential overlapping mechanisms between hallucinated and perceptual or retina-sourced bistability 74 new participants tracked alternations in binocular rivalry, a bistable rotating sphere (see Materials and methods) and the flicker-induced hallucinations. Figure 2H shows a scatter plot of the data, the rotating sphere (red) significantly predicted hallucinated alternation rates (r = 0.312; p=0.006), while binocular rivalry (blue) did not (r = 0.133; p=0.228). We propose that the predictive relationship between the rotating sphere and hallucinated bistability, but not rivalry, might be due to the former two both involving a common neurophysiological mechanism for motion.

Next we extend a model developed for full field flicker hallucination to explain both the constrained hallucinated content and its bistability (Rule et al., 2011). This model is based on the idea that uniform luminance flicker stimulation resonates with the natural frequency of cortical cells to evoke standing waves of activity in primary visual cortex that induce the conscious experience of the hallucination (Billock and Tsou, 2012; Rule et al., 2011; Ermentrout and Cowan, 1979).

We modeled the region of visual cortex that was stimulated by the flickering annulus as a ring of tissue in one spatial dimension (Figure 3A). The neural tissue was modelled using an established neural field model (see Appendix 1: Equations 1–3) comprising spatially-coupled populations of excitatory (E) and inhibitory (I) cells (Figure 3B, top). The standing waves/hallucinations arise when flicker frequencies are approximately twice the natural frequency of the damped oscillations in the neural dynamics (Rule et al., 2011). The resonant frequency of simple cells in the primary visual cortex of cat typically peaks near 5 Hz (Movshon et al., 1978). Here we tuned the natural frequency of the model to 5.5 Hz so that it elicited prominent standing waves with 11 Hz flicker to match our behavioral data (Figure 1D).

Figure 3 with 1 supplement see all

Download asset Open asset

Motion signals were then extracted from the space-time signatures of the standing waves in cortex using two banks of direction-selective motion detectors (Figure 3B, middle). These detectors (see Appendix 1: Equations 8–10) were implemented using Gabor filters (Jones and Palmer, 1987) according to the classic motion-energy model (Adelson and Bergen, 1985). Given that our interest was in hallucinated motion, we applied the motion-energy model directly to the cortical activity patterns rather than to the stimulus pattern. The output of the motion detectors within each bank were linearly combined to form a net motion-energy signal that represented the valence of motion in the detector’s preferred direction. These net motion signals were then fed into distinct neural populations that encoded the perceptual states of Left (counter-clockwise) and Right (clockwise) motion respectively (Figure 3B, bottom). Perceptual rivalry between these two neural populations was achieved through mutual inhibition and firing rate adaptation (see Appendix 1: Equations 11–13). Models of this class replicate spontaneous perceptual switching between ambiguous stimuli and the association of higher switching rates with higher stimulus contrast/energy (Laing and Chow, 2002; Shpiro et al., 2007; Wilson, 2003). Independent noise was injected into the LEFT and RIGHT neural populations to induce variability in the dominance times of the rival motion percepts.

When stimulated with 11 Hz uniform flicker (the stimulus parameters that gave the highest hallucinated contrast; Figures 1D and 3C), the model generated ‘cortical’ standing waves, that is, oscillations in modelled cortex, at half the flicker rate (Figure 3D), in accordance with previous findings. Standing waves were observed for flicker frequencies in the range 8–18 Hz, which we interpret as hallucinatory. Further, it was also possible to induce spatially irregular patterns by adding in weak random connections between the E cells shown in Figure 3B (data not shown). Beyond those frequencies the cortical model produced spatially uniform responses (Figure 3—figure supplement 1H) which we interpreted as non-hallucinatory. The space-time signatures of the flicker-induced standing waves evoked identical responses from both the Left and Right motion detectors (Figure 3E). Consequently, those ambiguous motion signals induced spontaneous switching between the two populations (Figure 3F). The dominance times of each perceptual decision (Figure 3G) exhibited a long-tailed distribution (M = 5.1 s, SD = 1.6 s) that was qualitatively similar to those observed experimentally (Figure 2B). However, it is interesting to note the differences in the shape-parameter (a) of the gamma fits, between the behavioral and model data. This difference could be summed up by describing the model data as being closer to a normal distribution than the behavioral data. One possible reason for the difference could be our choice of Gaussian noise in the rivalry model. Future work could probe different noise distributions to fine tune a model of bistable hallucinations.

When the same model is presented with a counter-phase retina-sourced physical patterned stimulus (Figure 3H), with identical spatial (fx = 0.11 cycles/mm) and temporal (ft = 5.5 Hz) frequencies to the flicker-induced standing waves (hallucinations), standing waves were also produced in model-cortex (Figure 3I; see Appendix 2). The net motion signals were stronger than those induced by the blank flicker stimulation (Figure 3E and J), hence the spontaneous switching between LEFT and RIGHT perceptual decisions was somewhat faster (M = 4.3, SD = 1.5, Figure 3K and L).

Our data implicate retinotopically organized visual cortex as the site of bistable flicker induced hallucinations. Unlike previous work on visual hallucinations that suffered methodological limitations due to the almost infinite array of unpredictable hallucinated features (e.g. multiple combinations of color, form and motion), our technique essentially limits the space to a one dimensional annulus and the one set of visual features: moving light grey blobs.

The intriguing phenomenon of perceptual bistability has fascinated thinkers for centuries (Blake and Logothetis, 2002), both because of the phenomenological experience of oscillating consciousness, but also as it provides the informative dissociation between low-level stimulation and awareness. Here we show a hallucinated bistable stimulus, in which both the content (form and motion) and alternations in motion are endogenously generated. Counter-phase physical stimuli are known to induce motion percepts that spontaneously switch between the two candidate directions of motion. Our model suggests that uniform flicker can induce spatiotemporal responses in primary visual cortex that are very similar to those induced by counter-phase physical stimuli, given the appropriate choice of spatial and temporal frequencies. We argue that the same neural mechanism that contributes to apparent motion of a counter-phase physical stimulus also contributes to hallucinated experience. It is up to future research to divulge if sensory decisions in endogenously generated content are resolved using the same neural machinery as exogenously sourced perceptual information.

A neural field model based on the idea that standing waves of neural activity form visual hallucinations, provided a quantitative mechanism for these bistable hallucinations. It is interesting that in general, theories based on so-called symmetry-breaking standing waves have been proposed to explain the complex spatio-dynamics of the human brain (Atasoy et al., 2016), as well as in many other physical processes such as convection in fluids, animal coat markings, and cellular division (Stewart, 1999; Turing, 1952; Kondo and Miura, 2010).

The exceptional circumstances in which externally sourced stimuli are overwhelmed by internally generated spontaneous patterns of neural activity and the accompanying conscious experience (hallucinations), are notoriously difficult to study scientifically. Accordingly, almost no specific treatments have been developed for clinical use. Our technique for controlling and objectively measuring the range of hallucinated features (contrast, motion, bistability) and the corresponding neural model should prove useful in probing the mechanism(s) that allows such a range of non-ordinary function to produce hallucinations.

1. 1. Adelson EH
   2. Bergen JR

   (1985) Spatiotemporal energy models for the perception of motion

   Journal of the Optical Society of America A 2:284–299.

   https://doi.org/10.1364/JOSAA.2.000284

   • Google Scholar
2. 1. Allefeld C
   2. Pütz P
   3. Kastner K
   4. Wackermann J

   (2011)

   Consciousness and cognition

   Consciousness and Cognition  20:1344–1362.

   • Google Scholar
3. 1. Anderson SJ
   2. Burr DC
   3. Morrone MC

   (1991) Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision

   Journal of the Optical Society of America A 8:1340–1351.

   https://doi.org/10.1364/JOSAA.8.001340

   • Google Scholar
4. 1. Atasoy S
   2. Donnelly I
   3. Pearson J

   (2016) Human brain networks function in connectome-specific harmonic waves

   Nature Communications 7:10340.

   https://doi.org/10.1038/ncomms10340

   • Google Scholar
5. 1. Aurora SK
   2. Wilkinson F

   (2007) The brain is hyperexcitable in migraine

   Cephalalgia 27:1442–1453.

   https://doi.org/10.1111/j.1468-2982.2007.01502.x

   • Google Scholar
6. 1. Barrett TR
   2. Etheridge JB

   (1994) Verbal hallucinations in normals—III: Dysfunctional personality correlates

   Personality and Individual Differences 16:57–62.

   https://doi.org/10.1016/0191-8869(94)90110-4

   • Google Scholar
7. 1. Barrett TR

   (1993) Verbal hallucinations in normals—II: Self-reported imagery vividness

   Personality and Individual Differences 15:61–67.

   https://doi.org/10.1016/0191-8869(93)90041-Z

   • Google Scholar
8. 1. Bentall RP

   (1990) The illusion of reality: a review and integration of psychological research on hallucinations

   Psychological Bulletin 107:82–95.

   https://doi.org/10.1037/0033-2909.107.1.82

   • Google Scholar
9. 1. Bidwell S

   (1897) On the negative after-images following brief retinal excitation

   Proceedings of the Royal Society of London 61:268–271.

   https://doi.org/10.1098/rspl.1897.0035

   • Google Scholar
10. 1. Billock VA
    2. Tsou BH

    (2012) Elementary visual hallucinations and their relationships to neural pattern-forming mechanisms

    Psychological Bulletin 138:744–774.

    https://doi.org/10.1037/a0027580

    • Google Scholar
11. 1. Blake R
    2. Logothetis N

    (2002) Visual competition

    Nature Reviews Neuroscience 3:13–21.

    https://doi.org/10.1038/nrn701

    • Google Scholar
12. 1. Blake R
    2. Sobel KV
    3. Gilroy LA

    (2003) Visual motion retards alternations between conflicting perceptual interpretations

    Neuron 39:869–878.

    https://doi.org/10.1016/S0896-6273(03)00495-1

    • Google Scholar
13. 1. Butler TC
    2. Benayoun M
    3. Wallace E
    4. van Drongelen W
    5. Goldenfeld N
    6. Cowan J

    (2012) Evolutionary constraints on visual cortex architecture from the dynamics of hallucinations

    PNAS 109:606–609.

    https://doi.org/10.1073/pnas.1118672109

    • Google Scholar
14. 1. Ermentrout GB
    2. Cowan JD

    (1979) A mathematical theory of visual hallucination patterns

    Biological Cybernetics 34:137–150.

    https://doi.org/10.1007/BF00336965

    • Google Scholar
15. 1. Ffytche DH

    (2008) The hodology of hallucinations

    Cortex 44:1067–1083.

    https://doi.org/10.1016/j.cortex.2008.04.005

    • Google Scholar
16. 1. Horton JC
    2. Hoyt WF

    (1991) The representation of the visual field in human striate cortex. A revision of the classic Holmes map

    Archives of Ophthalmology 109:816–824.

    https://doi.org/10.1001/archopht.1991.01080060080030

    • Google Scholar
17. 1. Hubel DH
    2. Wiesel TN

    (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex

    The Journal of Physiology 160:106–154.

    https://doi.org/10.1113/jphysiol.1962.sp006837

    • Google Scholar
18. 1. Jones JP
    2. Palmer LA

    (1987)

    An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex

    Journal of Neurophysiology 58:1233–1258.

    • Google Scholar
19. 1. Kilpatrick ZP

    (2013)

    Encyclopedia of Computational Neuroscience, 1-5

    Wilson-cowan model, Encyclopedia of Computational Neuroscience, 1-5, New York, NY, Springer New York, 10.1007/978-1-4614-7320-6_80-1.

    • Google Scholar
20. 1. Kondo S
    2. Miura T

    (2010) Reaction-diffusion model as a framework for understanding biological pattern formation

    Science 329:1616–1620.

    https://doi.org/10.1126/science.1179047

    • Google Scholar
21. 1. Laing CR
    2. Chow CC

    (2002) A spiking neuron model for binocular rivalry

    Journal of Computational Neuroscience 12:39–53.

    https://doi.org/10.1023/A:1014942129705

    • Google Scholar
22. 1. Llinás R
    2. Ribary U

    (1993) Coherent 40-Hz oscillation characterizes dream state in humans

    PNAS 90:2078–2081.

    https://doi.org/10.1073/pnas.90.5.2078

    • Google Scholar
23. 1. Mauro F
    2. Raffone A
    3. VanRullen R

    (2015) A bidirectional link between brain oscillations and geometric patterns

    Journal of Neuroscience 35:7921–7926.

    https://doi.org/10.1523/JNEUROSCI.0390-15.2015

    • Google Scholar
24. 1. Movshon JA
    2. Thompson ID
    3. Tolhurst DJ

    (1978) Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex

    The Journal of Physiology 283:101–120.

    https://doi.org/10.1113/jphysiol.1978.sp012490

    • Google Scholar
25. 1. Passie T
    2. Halpern JH
    3. Stichtenoth DO
    4. Emrich HM
    5. Hintzen A

    (2008) The pharmacology of lysergic acid diethylamide: a review

    CNS Neuroscience & Therapeutics 14:295–314.

    https://doi.org/10.1111/j.1755-5949.2008.00059.x

    • Google Scholar
26. 1. Pearson J
    2. Brascamp J

    (2008) Sensory memory for ambiguous vision

    Trends in Cognitive Sciences 12:334–341.

    https://doi.org/10.1016/j.tics.2008.05.006

    • Google Scholar
27. 1. Rule M
    2. Stoffregen M
    3. Ermentrout B

    (2011) A model for the origin and properties of flicker-induced geometric phosphenes

    PLoS Computational Biology 7:e1002158.

    https://doi.org/10.1371/journal.pcbi.1002158

    • Google Scholar
28. 1. Shapley R

    (1990) Visual sensitivity and parallel retinocortical channels

    Annual Review of Psychology 41:635–658.

    https://doi.org/10.1146/annurev.ps.41.020190.003223

    • Google Scholar
29. 1. Shpiro A
    2. Curtu R
    3. Rinzel J
    4. Rubin N

    (2007) Dynamical characteristics common to neuronal competition models

    Journal of Neurophysiology 97:462–473.

    https://doi.org/10.1152/jn.00604.2006

    • Google Scholar
30. 1. Stewart I

    (1999) Mathematics: Holes and hot spots

    Nature 401:863–865.

    https://doi.org/10.1038/44730

    • Google Scholar
31. 1. Suzuki S
    2. Grabowecky M

    (2007) Long-term speeding in perceptual switches mediated by attention-dependent plasticity in cortical visual processing

    Neuron 56:741–753.

    https://doi.org/10.1016/j.neuron.2007.09.028

    • Google Scholar
32. 1. Turing AM

    (1952) The chemical basis of morphogenesis

    Philosophical Transactions of the Royal Society B 237:37–72.

    https://doi.org/10.1098/rstb.1952.0012

    • Google Scholar
33. 1. Wagner G
    2. Boynton RM

    (1972) Comparison of four methods of heterochromatic photometry

    Journal of the Optical Society of America 62:1508–1515.

    https://doi.org/10.1364/JOSA.62.001508

    • Google Scholar
34. 1. Wilson HR
    2. Blake R
    3. Lee SH

    (2001) Dynamics of travelling waves in visual perception

    Nature 412:907–910.

    https://doi.org/10.1038/35091066

    • Google Scholar
35. 1. Wilson HR
    2. Cowan JD

    (1972) Excitatory and inhibitory interactions in localized populations of model neurons

    Biophysical Journal 12:1–24.

    https://doi.org/10.1016/S0006-3495(72)86068-5

    • Google Scholar
36. 1. Wilson HR
    2. Cowan JD

    (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

    Kybernetik 13:55–80.

    https://doi.org/10.1007/BF00288786

    • Google Scholar
37. 1. Wilson HR

    (2003) Computational evidence for a rivalry hierarchy in vision

    PNAS 100:14499–14503.

    https://doi.org/10.1073/pnas.2333622100

    • Google Scholar

Author details

1. Joel Pearson

   The School of Psychology, University of New South Wales, Sydney, Australia

   Contribution

   JP, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents

   For correspondence

   jpearson@unsw.edu.au

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0003-3704-5037

2. Rocco Chiou

   The School of Psychology, University of New South Wales, Sydney, Australia

   Contribution

   RC, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

3. Sebastian Rogers

   The School of Psychology, University of New South Wales, Sydney, Australia

   Contribution

   SR, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

4. Marcus Wicken

   The School of Psychology, University of New South Wales, Sydney, Australia

   Contribution

   MW, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

5. Stewart Heitmann

   Department of Mathematics, University of Pittsburgh, Pittsburgh, United States

   Contribution

   SH, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

6. Bard Ermentrout

   Department of Mathematics, University of Pittsburgh, Pittsburgh, United States

   Contribution

   BE, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents

   Competing interests

   The authors declare that no competing interests exist.

• 17,241

  views

• 693

  downloads

• 27

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.