Introduction

A colour afterimage arises, when an observer fixates a coloured area over a sustained period1,2. Through this exposure, the underlying neural mechanisms of colour processing adapt and become insensitive to the colour of that area, the inducer. These mechanisms remain most sensitive to the colour that is least similar to the inducer and produce a complementary (or negative) afterimage when replacing the inducer by a colourless grey area. For example, if you fixate on a yellow circle, when taken away you will see a blue-purple circle even though the circle’s area is now physically the same as the colourless surround (see Supplementary Movie 1 and section A.1 Illustration of Afterimages of the Supplementary Material). The underlying mechanisms of temporal adaptation to colour enable us to reliably perceive colour even though lighting constantly changes in our everyday environment. Illusory afterimages have thus been used to disseminate the most fundamental tenets of human colour perception in reviews, textbooks, and other broader communications, including the concepts of chromatic adaptation and colour constancy, colour opponency and complementarity, and the dependence of colours on the context and the beholder3,4,5,6,7,[8](https://www.nature.com/articles/s44271-025-00331-5#ref-CR8 “Conway, B. R., Malik-Moraleda, S. & Gibson, E. Color appearance and the end of Hering’s Opponent-Colors Theory. Trends Cognit. Sci., https://doi.org/10.1016/j.tics.2023.06.003

(2023).“).

Although candidate mechanisms of adaptation have been known for more than a century9, state-of-the-art explanations of this important phenomenon remain contradictory and confused. Human colour perception is the result of several stages of processing, starting with the excitation of the cone photoreceptors in the eyes, propagating through cone-opponent mechanisms in the retinal ganglion cells, the LGN of the thalamus, and the single- and double-opponent cells in the primary visual cortex, until the colour signal reaches higher cortical areas that produce the subjective experience of colour10. Evidence for adaptation has been found at many points along this visual hierarchy. Adaptation of photoreceptors at the first stage of colour processing produces divisive adaptation, similar to von Kries’ original proposal9, and can be approximated by contrast coding following Weber’s law11,12,13,14,15,16. A slower type of “second-site adaptation” occurs in the retinal ganglion cells17, and is assumed to be subtractive11,18,19,20. Other observations suggested “higher-order” adaptation of cortical mechanisms3,21,22,23,24.

Researchers have disagreed about the neural mechanisms of adaptation that cause complementary afterimages6,20,25,[26](https://www.nature.com/articles/s44271-025-00331-5#ref-CR26 “Alzeer, M. S., Houwers, K., van de Smagt, M., Van der Stigchel, S. & Naber, M. After-image formation by adaptation to dynamic color gradients. Attention, Percep. Psychophys. https://doi.org/10.3758/s13414-022-02570-8

(2022).“). Classical studies suggested that such afterimages are caused by photoreceptor desensitisation (“cone bleaching”) at the first stage of processing27,28,29,30,31. Later studies firmly contradicted this idea20,32,33, attributed afterimages to adaptation in the cone-opponent channels of the second stage20,32,34, or emphasised the effects of cortical adaptation33,35,[36](#ref-CR36 “Zeki, S., Cheadle, S., Pepper, J. & Mylonas, D. The constancy of colored after-images. Front. Hum. Neurosci. 11, https://doi.org/10.3389/fnhum.2017.00229

(2017).“),37,38,39,[40](#ref-CR40 “Powell, G., Bompas, A. & Sumner, P. Making the incredible credible: afterimages are modulated by contextual edges more than real stimuli. J. Vis. 12, https://doi.org/10.1167/12.10.17

(2012).“),41,42,[43](https://www.nature.com/articles/s44271-025-00331-5#ref-CR43 “Dong, B., Holm, L. & Bao, M. Cortical mechanisms for afterimage formation: evidence from interocular grouping. 7, 41101 https://doi.org/10.1038/srep41101

(2017).“). Even more importantly, the link between neural mechanisms and the perceived colours of afterimages has been ignored or misconstrued. Irrespective of the hypothesised neural origin, most state-of-the-art research assumes that the perceived colours of afterimages are cone-opponent20,34,[36](https://www.nature.com/articles/s44271-025-00331-5#ref-CR36 “Zeki, S., Cheadle, S., Pepper, J. & Mylonas, D. The constancy of colored after-images. Front. Hum. Neurosci. 11, https://doi.org/10.3389/fnhum.2017.00229

(2017).“),38,44, but there is evidence against that assumption25,45. As a result of this confusion, textbooks, reviews, and other broader communications either do not attempt any explanation of colour afterimages2,4 or disseminate misleading narratives, such as the idea that afterimages reflect Hering-opponency between red/green and blue/yellow6,[8](https://www.nature.com/articles/s44271-025-00331-5#ref-CR8 “Conway, B. R., Malik-Moraleda, S. & Gibson, E. Color appearance and the end of Hering’s Opponent-Colors Theory. Trends Cognit. Sci., https://doi.org/10.1016/j.tics.2023.06.003

(2023).“).

This study leveraged the fact that adaptation of mechanisms at different stages along the hierarchy of colour processing make markedly different quantitative predictions about the colours of complementary afterimages (Fig. 1). Predicted hue and chroma of afterimages differ across models. Hue describes how reddish, yellowish, greenish, and bluish a colour is. Chroma refers to the colourfulness of a hue. At equal brightness (isoluminance), it is equivalent to saturation and corresponds to the difference of a colour from grey. Using tailormade experimental paradigms, the exact colours perceived in afterimages were measured for a large range of inducers to test those predictions. Three comprehensive experiments unambiguously showed that the colours of afterimages tightly follow the non-opponent predictions that are specific to cone adaptation.

Fig. 1: Afterimage stimuli and models.

In all panels, colours are represented in CIELUV colour space; see Fig. S11 of the Supplementary Material for analogous diagrams in cone-opponent DKL space. a illustrates the stimulus samples in Experiment 1a (coloured lines), Experiment 1b (black circles), and Experiment 2a (black circles and dots). In Experiment 2b stimuli were sampled along a hue circle as in Experiment 2a, but in DKL instead of CIELUV (Fig. S11*.*a). b shows the results of cone-adaptation without (red line) and with noise (black dots); the noise was used for modelling hue histograms. c illustrates adaptation of the cone-opponent channels, where the afterimage is shifted to the hue opposite to the inducer hue (thick red line). For comparison, predictions based on adaptation in CIELUV space (thin black line) are also shown. CIELUV predictions of hue are the same as for cone-opponency DKL space but predicted chroma differs from cone-opponent predictions. d illustrates predictions of CIECAM02 (thick red line) and CIELAB (thin black line), which are common models of colour appearance. e illustrates Hering-opponency (black) and opponency in the Munsell colour system (red). The coloured lines in the background correspond to measured red, yellow, green, and blue. Two cone-opponent examples of inducers (60 and 240°) are shown in (b–e). The crossing point between lines and hue circle indicates the inducer, large dots indicate the colour of the corresponding afterimage predicted by the respective model. Lines and dots are shown in the inducer colour. For first-person inspection, the yellowish inducer (60°) corresponds to the inducer in Supplementary Movie 1.

Methods

Experiment 1 was approved by the ethics committee at the University of Gießen (LEK 2017-0030). Experiments 2 and 3 were approved by the Faculty Ethics Committee at the University of Southampton, ERGO 65442. All participants provided informed consent prior to participating. None of the experiments were preregistered. All information about sex is provided by participants.

Experiment 1: Fixed-Location Afterimages

Participants

In Experiment 1a, 31 observers participated (25 women and 6 men, age: M = 25.9 ± SD = 4.2 years). In Experiment 1b, 52 observers took part (36 women and 16 men, age: 25.1 ± 4.3 years). Participants were compensated by course credits or €8 per hour. Colour vision deficiencies were excluded using the HRR plates46.

Apparatus

Stimuli were presented on an Eizo Colour Edge Monitor (36.5 × 27 cm) with an AMD Radeon Firepro graphics card with a colour resolution of 10 bits per channel. The CIE1931 chromaticity coordinates and luminance (xyY) of the monitor primaries were R = (0.6847, 0.3111, 26.4), G = (0.2138, 0.7263, 69.9), and B = (0.1521, 0.0453, 4.8). Gamma was 2.2 for all channels and has been corrected.

Stimuli

Colours were represented in CIELUV space. The white-point was xyY = [0.3304, 0.3526, 101.1], background lightness was L* = 70. At isoluminance, opponent hues in CIELUV are the same as cone-opponent hues in Derrington-Krauskopf-Lennie (DKL) space47 (Fig. 1a) and as opponent hues determined along lines in (gamma-corrected) HSV and RGB space6,25, tristimulus values (XYZ) and chromaticity coordinates (xyY); see sections E.2-3 of the Supplementary Material for mathematical details45. CIELUV space was preferred to DKL space because it better controls for perceived chroma48,49. The eight inducer colours in Experiment 1a were chosen to correspond to the typical lightness and hue of red, orange, yellow, green, turquoise, blue, purple, and magenta at the maximum chroma possible within monitor gamut (coloured lines in Fig. 1a). The nine hues of the comparison colours (cf. Procedure) were obtained by adding four hues in 10-degree (deg) steps to either direction (low or high azimuth) of the opponent hue. Lightness and chroma of the comparisons were determined through piloting. In Experiment 1b, twenty-four inducers were sampled along a hue circle in CIELUV at chroma 71 and equal steps of 15 deg starting at 0 deg (black circles in Fig. 1a). Chroma was chosen to be the highest chroma achievable within monitor gamut for all hue directions. Lightness of inducers, comparison colours, and the achromatic disc in the centre of the test display were the same as the background (L* = 70). This brightness corresponds to 1.7% cone bleaching according to the Rushton and Henry half-bleach constant50. Hues of comparison colours were determined as in Experiment 1a and chroma was kept constant at 30 for all comparison colours. This level of chroma was determined through piloting and accounts for the lower saturation of the afterimages compared to the inducers. Table S2 in the Supplementary Material provides detailed colour specifications.

Procedure

In each trial, the inducer display (Fig. 2a) was shown for 20 s (Experiment 1a) and 30 s (Experiment 1b). A cover task ensured that the observer fixated a dot in the centre (details in section B.2 Details on Afterimage measurements of the Supplementary Material). After this adaptation period, observers determined which of the nine comparisons was the closest match to the afterimage colour while seeing the afterimage in the centre (Fig. 2a). Afterimages appeared to ‘melt into’ the segment with the colour that looked closest to the afterimage, making the task intuitive. Participants used the mouse to indicate the segment with the matching comparison. If they could not see any of the comparison colours in the centre, they could also click on the centre disk to indicate this and skip the trial (resulting in a missing value). A 10-s intertrial display followed by a self-parsed break was used to cancel remaining afterimages and to prevent afterimage interference across trials (see section B.2 Details on Afterimage measurements of Supplementary Material). The order of trials was randomised. In Experiment 1a, trials were repeated across four blocks. Few trials were skipped (about 2% in both parts).

Fig. 2: Experiment 1-2.

The first row (a–d) illustrates stimulus displays and task (a), and results (c, d) for Experiment 1. Observers adapt to the inducer display for 30 s (yellow in a). Then the inducer display is replaced by a circle of background grey together with nine comparison colours (purple in a) in a circular arrangement around the grey circle. The grey circle in the centre is perceived as the induced afterimage, and observers select the comparison colour that best matches the colour they see in the centre. b gives examples of afterimage matches averaged across N = 31 participants in Experiment 1a with maximally saturated colours. Discs correspond to inducers, stars to average matches of perceived afterimages. The thin line in the background indicates the cone-opponent direction, the dashed line the prediction of the cone-adaptation model (see Figs. S2a and S3 for results with the other four colours). c, d illustrate results from N = 52 participants in Experiment 1b. The second row (e–h) corresponds to Experiment 2a with the chaser-like paradigm. In (e), the chromatic ring is the inducer. Participants fixate the centre, and the moving grey circle on the ring reveals the afterimage. Observers adjusted hue and chroma of the centre circle to match the moving one. Average afterimage matches from N = 10 participants and overall N = 45 measurements per colour (black curve in f) closely correspond with predictions by cone adaptation (red outline), yielding a correlation (bottom left) between measured and simulated afterimage intensity (i.e., chroma) across the N = 72 inducer colours. The curves in the third column (c, g) show the deviation of the cone-adaptation model (red curve) and of the measured afterimages (black curve) from the colours opponent to the inducers. Correlations between simulated and measured deviations from opponency are shown at the bottom of the diagrams. The correlation reflects the high similarity in profile of the two curves. The hue histograms in the last column (d, h) counts hue responses (azimuth in f) and displays the resulting frequencies as a function of azimuth in a polar plot. The histogram of the measurements is shown by the grey area in the background, and the histogram of the simulated afterimages by the red outline. Panel d provides the hue histogram for the N = 52 measurements for 24 colours in Experiment 1b and (h) those for the N = 45 measurements for 72 inducer colours in Experiment 2a. In (h), a smoothed version of the hue histogram is shown by the black line. Hue histograms feature three clusters that closely correspond with model predictions (red line), hence confirming the results from (c, f, g). Additional results from Experiment 2b with stimuli in DKL space are provided by Fig. S12 of Supplementary Material. The last row illustrates average deviations of different model predictions from measured afterimage hue (i) and chroma (j). The top and bottom edges of each box are the upper and lower quartiles, the line inside each box is the median; whiskers are the minimum and maximum values that are not outliers, and dots outside the whiskers are outliers identified as values outside the interquartile range (box) by 1.5 times the size of the interquartile range. The grey symbols (Noise) provide estimates of noise calculated as the average difference of each individual’s measurement from the group mean (interindividual variation) in Experiment 1 and of each single measurement from the mean of each participant (intraindividual variation) in Experiment 2. Chroma has been z-scored to focus on relative differences across hues. Supplementary Movies 1–4 visualise the differences between opponent and afterimage hues (see also section A and Fig. S1 of Supplementary Material).

Colour naming and control task

For details about the measurement of colour categories and prototypes and about the control task, see sections B.3-4 of the Supplementary Material.

Experiments 2-3: Chaser-Like Afterimages

Tables S3 and S4 in the Supplementary Material provide details about participants and apparatus in Experiments 2 and 3. Supplementary Movies 1–4 and section A.2 Illustration of the Method in Experiments 2-3 in the Supplementary Material provide a simplified illustration of the tasks in Experiments 2 and 3.

Participants

Ten volunteer participants (6 women, and 4 men, age: M = 23.4 ± SD = 8.3 years), including the author (CW, male, 43 years old) took part (cf. Table S4) in Experiment 2a. Three more observers had started one round of measurements (8 hues) but did not come back to complete a sufficient dataset for all 72 hues. CW and a naïve, 37-year-old female observer (f1) participated in Experiment 2b (cf. Table S4). In Experiment 3, measurements across chroma were done by the author (CW), and four naïve female, 19-year-old participants (Table S5).

Apparatus and stimuli

Three different experimental set-ups were used in Experiments 2–3 and calibrated as explained for Experiment 1 (Table S4–S5). All measurements were conducted in ambient darkness. Figure 2e illustrates the stimulus display (see also Supplementary Movies 1–4 and Fig. S1). In Experiment 2a, 72 inducer colours were sampled in 5-deg hue steps along an isoluminant hue circle at L* = 70 in CIELUV-space. This sampling resolution is almost exhaustive, considering that hue discrimination thresholds are larger than 5 degrees48. The brightness corresponded to about 3–3.5% cone bleaching according to the Rushton and Henry half-bleach constant50. Inducer chroma was set to be maximal within the respective monitor gamut, resulting in a chroma of 38 (one participant), 42 (two participants), or 50 (everyone else); for details see Table S4. In Experiment 2b, the sampling was done along an isoluminant hue circle in DKL space with a radius of 0.5 (CW) and 0.7 (f1), as illustrated by Fig. S11 of the Supplementary Material. The chromatic axes were scaled relative to the monitor gamut to avoid gamut artefacts (see section E.2 Cone-Opponent Model (DKL) of the Supplementary Material for mathematical details). For measurements across chroma in Experiment 3 (Fig. 3), additional chroma levels were measured at 20, 30, and maximum within gamut (see Table S5 for details).

Fig. 3: Change of Afterimage Hue with Chroma (Experiment 3).

a Visualisation of the effect of inducer chroma on afterimage hue. Numbers in the coloured rectangles indicate hue. Rows correspond to example inducer stimuli of constant hue (60 deg) and different chroma levels (20–70), the cone-opponent hue (240 deg), the prediction by cone-adaptation with varying hue, and the average hue of the prediction that is used for the analyses. The variation in chroma predicted by cone adaptation has been ignored here to facilitate the visual comparison of hue changes. b N = 216 inducer stimuli (coloured dots) varying across three levels of chroma (20, 50, maximum). The grey circles in the background indicate chroma (radius) varying from 10 to 80 in steps of 10. The doted tetragon shows the monitor gamut at that luminance level. c Afterimages modelled through cone contrasts. The black lines illustrate how afterimages vary when inducer chroma corresponds to the grey circles. Coloured dots indicate simulated afterimages for measurements with the N = 216 inducer stimuli of (b). d Comparison between measurements and cone-adaptation predictions. Grey dots are the N = 216 measurements; thick transparent black lines highlight the change across chroma for hues at 45-deg intervals. Grey lines indicate the reference average used to calculate hue-specific chroma differences. Red lines show the corresponding cone-adaptation predictions. e, f Scatterplots illustrating the correlation between simulated and measured changes of afterimage hue across chroma. The axes indicate the afterimage hue difference from the cone-opponent hue (e) and from the reference average (f) in azimuth degree. Dot colours indicate inducer colours. This figure shows results for observer f7. Results for four other observers can be found in Table 4 and Fig. S13, each replicating these results.

Procedure

In each trial, participants were asked to fixate the centre of the display until the moving circle reached maximum colourfulness. Then, they used the cursor keys to adjust the hue (left/right) and saturation (up/down) of the centre circle. The initial colour of this circle was set to a random hue at inducer chroma. During a coarse adjustment, participants could continuously change colours; but before confirming the adjusted colour, participants needed to do a fine adjustment (by holding space). In the fine adjustment, the colour changes by single steps (in radius or in 1 deg azimuth) with each separate key press.

Since the adjustment takes time, observers would see afterimages from the adjusted colour attenuating the perceived chroma of the adjusted colour. Two measures were taken to avoid this: During coarse adjustment, black and white circles (not areas) were extending from the centre of the adjusted disk to its rim. These circles would disappear during fine adjustments to avoid interference with the finalised match. In addition, holding the control key would turn the centre disk temporarily into grey until the key was released. Observers were asked to wipe out unwanted afterimages from the adjusted centre disk using that key before confirming the adjustment. So, they would hold control, wait and move their eyes until the centre disk appeared achromatic. They would then stare at the grey circle until the moving circle reached maximum chroma. Only then would they release the key and compare the colour they had previously adjusted with the colour of the moving circle. Typically, the adjusted colour was too saturated due to the overlaying of its own afterimage during the adjustment. So, participants needed to lower chroma after readaptation. They reiterated this procedure until the chroma did not need adjustment after releasing the control key. Only then did participants confirmed their adjustments by pressing enter. As in Experiment 1, an intertrial period was used to prevent afterimage carry-over across trials.

Inducer colours were split into nine series of eight colours. Within a series, the eight colours were separated by 45 degrees in azimuth. Different series were defined by different starting points (0, 5, 10…40 degree) so that the series together covered all 72 inducers. Each block of measurements featured one trial for each of eight inducer colours in a series, presented in random order. Measurements of each block were repeated up to five times (cf. Figs. S8–10). Blocks of measurements were spread over several days. Prior to measurements, participants were trained with practice blocks with the presence and feedback of the experimenter (CW) to make sure they understood task handling and the aim of measuring the illusory afterimage colour as precisely as possible.

Models

With all models, the colour signal of the grey probe circle (same as background colour) was calculated under local adaptation to the inducer. Then, the colour of the resulting afterimage was determined as the locally adapted colour signal under global adaptation to the grey background. The known fact that afterimages are not as saturated as inducers (Fig. 2f) implies that adaptation to inducers is not complete. As an estimate of the strength of adaptation, adapting chroma for modelling afterimages was set to the chroma of the comparison colours in Experiment 1, and to the grand average chroma (27.0 in CIELUV and 0.47 in DKL) of adjustments in Experiment 2. Even if complete adaptation to the chroma of inducers had been assumed, results would be largely the same. However, not surprisingly, correlation coefficients involving cone adaptation would be slightly lower because non-linearities in the model are then higher than in the measurements. There are no free parameters in any of the models.

First-stage adaptation

Cone adaptation at the first stage of colour processing was modelled by cone contrasts11,12,13,14,15,16. Cone contrasts (CC) are Weber fractions, calculated as the difference between cone excitations of the stimulus (LMS) and cone excitations of the adapting colour (LMS0) relative to the cone excitations of the adapting colour: CC = (LMS-LMS0)/LMS0. Cone contrast is calculated independently for the short- (S), medium- (M), and long-wavelength (L) sensitive cones, resulting in S-cone, M-cone, and L-cone contrasts. In psychophysical experiments, adaptation is typically controlled by the colour of the background, which is then LMS0. To compute the induced colour of the afterimage, the roles are swapped because afterimages correspond to the perception of the achromatic background after local adaptation to the inducer. Local adaptation to the inducer is modelled by inserting the cone excitations of the inducer, iLMS, instead of the background into LMS0. As the afterimage is elicited on a grey probe, LMS now corresponds to bgLMS, i.e., the achromatic, isoluminant grey of the background:

(1) Cone adaptation to inducer:

$${{CC}}_{{LMS}}=\frac{{bg}{LMS}-i{LMS}}{i{LMS}}$$

Where bgLMS and iLMS refer to Stockman-Sharpe cone excitations of the grey background and the adapting inducer. Cone excitations were scaled to match the luminous efficiency function51. Cone contrast changes with increasing cone adaptation iLMS according to a multiplicative inverse function (because iLMS increases in the denominator). This adaptation produces shifts towards the peak cone sensitivities (Fig. 1b, Fig. S14).

Second-stage adaptation

Cone-opponency has been modelled with DKL colour space47. Details on the computation of the cone-opponent axes are provided in section E.2 Cone-Opponent Model (DKL) of the Supplementary Material. Cone-opponent adaptation is assumed to be subtractive11,19. So, it was calculated by subtracting the cone-opponent signal of the adapting colour from the cone-opponent signal of the achromatic probe20.

(2) Cone-opponent adaptation to inducer:

$${{DKL}}_{L-M}={bg}{{DKL}}_{L-M}-k* i{{DKL}}_{L-M}$$

$${{DKL}}_{S}={bg}{{DKL}}_{S}-k* i{{DKL}}_{S}$$

Where DKLL—M and DKLS are the adapted cone-opponent signals of L–M and S mechanisms, respectively, and bgDKL and iDKL are the cone-opponent signal of the background and inducer, respectively. The constant k indicates the strength of adaptation. As the background is achromatic, bgDKL is 0 in all channels, and the equations can be simplified to:

$${{DKL}}_{L-M}=-k* i{{DKL}}_{L-M}$$

$${{DKL}}_{S}=-k* i{{DKL}}_{S}$$

Therefore, cone-opponent adaptation produces proportional shifts along the DKL axes, predicting cone-opponent afterimage hues to be 180 degrees rotated away from the inducer and afterimage chroma that is k times the inducer chroma. Here, k was set to match the estimated strength of the afterimages, but the value of k was irrelevant to the results. At isoluminance, the cone-opponent mechanisms can be expressed as a function of cone-contrasts, resulting in:

$${DKL}_{L-M}=-({iCC}_{M}-{iCC}_{L})$$

$${{DKL}}_{S}={-{iCC}}_{S}$$

Where iCC is the cone contrast of the inducers calculated with equation (1), and the index indicates the respective cone (see section E.2 Cone-Opponent Model (DKL) of the Supplementary Material). Although a theoretically complete model would differentiate between the two separate mechanisms that constitute each opponent channel (“half-wave rectification”), such a separation did not change the predictions in this study.

Adaptation of colour appearance

Predictions by colour appearance models (CIELUV, CIELAB, CIECAM02) were computed as the colour appearance of the grey background when the adapting white-point was the inducer, using the respective adaptation transform. At isoluminance, CIELUV is a projective transformation of DKL space and involves a subtractive adaptation, which explains the identity of predicted hues. Sections E3-E5 in the Supplementary Material provide mathematical details and explanations. For predictions by Munsell and Hering colours, opponent colours were determined in the respective coordinate systems, which is equivalent to the effects of subtractive adaptation. Opponent colours in the Munsell system were interpolated using the CIELAB coordinates of the Munsell renotation table52 as provided by the Munsell Lab of the Rochester Institute of Technology. Details about the interpolations are provided in section E.6 Munsell-Opponent Model of the Supplementary Material. Hering-opponent colours were calculated by linearly interpolating the hue direction between the respective two empirically measured prototypes for red, yellow, green, and blue in CIELUV space. There was no prediction for Hering chroma. For details, see section E.7 Hering Opponent Model of the Supplementary Material.

Data distributions

Measurements of hue and chroma were approximately normally distributed across repeated measurements and participants, as checked by histograms (Figs. S3–S5) and normal probability plots (Figs. S6–S7).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Results

Figure 1 illustrates the colour stimuli (Fig. 1a), and the corresponding predictions of afterimage hue and chroma by candidate models of afterimages (Fig. 1b–e). Predictions for cone adaptation were computed with the mathematical model of Weber’s law11,12,13,14,15,16. Using the inducer as the adapting colour produces the triangular shape of the red curve in Fig. 1b. The triangular shape results from the predicted colour being dominated by the least-adapted cone due to the multiplicative inverse effects of cone adaptation (cf. Method and Fig. S14). This triangular shape means that cone adaptation contradicts the wide-spread assumption that afterimages are cone-opponent. In contrast, cone-opponent afterimages result from subtractive, second-site adaptation, as illustrated by the red circle in Fig. 1c. Alternative models have been proposed to better predict several aspects of colour appearance than those physiological models. They might better match the colour appearance of afterimages, too. CIELUV, CIELAB, and CIECAM02 implement complex, nonlinear models to approximate various empirical data on colour appearance7. At isoluminance (as here), CIELUV predicts the same afterimage hues as cone-opponency, but different afterimage chromas (Fig. 1c; cf. Method)48,[49](