Abstract
Anaglyphs are displays in which the left and right eye images are presented in different colours, such as red and cyan, and they are viewed through filters of the same colours so that each eye sees a different image. They have typically been used to present slightly different images to each eye so that they are seen in relief – stereoscopic depth. Anaglyphs have become increasingly popular as a means for printing and projecting stereoscopic drawings and photographs. The general standard now is for red/left eye, cyan/right eye filters for viewing similarly coloured printed or projected images and these are recommended for viewing the anaglyphs in this article. Despite the disdain for anaglyphs in visual science, they have been used extensively in visual art and education. However, anaglyphs can be constructed that yield displays that would be difficult to produce for refracting or reflecting stereoscopes.
How to Cite this Article
Wade, NJ. (2026). In praise of anaglyphs. i-Perception, 17(3), 1–26. https://doi.org/10.1177/20416695261448396
Introduction
There are several ways in which paired pictures can be observed to yield stereoscopic depth. The simplest is free viewing where adjacent pictures, equivalent to what is seen by the left and right eyes, are superimposed by adjusting the directions in which the eyes are pointing; with parallel viewing the left pattern is seen by the left eye and the right pattern by the right eye whereas with crossed convergence the reverse occurs. Wheatstone (1838) was able to view his stereograms in these ways but he found that many others to whom he showed them could not. It was for them that he invented the stereoscope which made the superimposition of the left- and right-eye images much easier. Reflecting and refracting stereoscopes were made for Wheatstone in 1832 (see Wade, 1983), although he did not publish his account of the mirror stereoscope until 1838 and of the prism version 14 years later (Wheatstone, 1852). The use of colours for separating the eyes to see depth was described by Rollmann (1853). D’Almeida (1858) achieved a similar effect using images projected with two magic lanterns having colour filters in front of the lenses; the observer viewed the superimposed projections through similar filters, one for each eye. He found that combinations of red and green projections and viewers worked well. Ducos du Hauron devised a method of over-printing red and blue or green designs in 1891 (see Ducos du Hauron, 1897) and it was referred to as the art of the anaglyph. Thereafter, anaglyphs became increasingly popular as a means for printing and projecting stereograms. Computer software for separating and combining the half-images has improved markedly relative to the early anaglyphs (Rádo et al., 2020; Templin, 2016) and anaglyphs are being used increasingly in stereo computer graphics (Qi et al., 2021; Sanders & McAllister, 2003). The anaglyphs shown here were composed using StereoPhoto Maker software (https://stereo.jpn.org/eng/stphmkr/) which incorporates the anaglyph algorithm devised by Dubois (2001). The software combines the two half-images with colour separations to match those of red and cyan viewers and enables adjustments to their alignment and sizes prior to producing the final anaglyph. Colours are retained in the anaglyphs but they do not match those in the original images from which the anaglyphs were constructed.
A natural consequence of viewing the world involves small differences in the projections to each eye because they are laterally separated by about 63 mm. The small differences between the projections to each eye are combined to give us stereoscopic depth perception. Large differences result in binocular rivalry – competition between the eyes rather than cooperation. Thus, anaglyphs are simple forms of stereoscopes: they provide a technique for presenting different patterns to each eye. Stereoscopes were devised to simulate what we naturally see with two eyes and they have been used to give us the impression of depth from two slightly different images presented to the eyes or rivalry between radically different ones (see Blundell, 2011; Howard & Rogers, 1995). These two facets of binocular vision are evident in Figure 1. The surrounds of the schematic eyes are either in correspondence or in rivalry as is the case for the centres.
Stereoscopic depth and binocular rivalry by Nicholas Wade. Viewing the anaglyphs with red/left eye and cyan/right eye results in all the central discs appearing closer than the surrounds; reversing the filter/eye viewing reverses the apparent depths of the central discs. The directions and extents of the depths appear similar irrespective of the fusion or rivalry of the central discs.
Anaglyphs
Anaglyphs have not proved popular for use in experimental studies of stereoscopic vision, and for good reason. Howard and Rogers (1995, 2002, 2012), in their compendious volumes on binocular vision and stereopsis, cite very few studies employing anaglyphs relative to those using reflecting and refracting stereoscopes (which will be referred to as optical stereoscopes hereafter). They note: ‘There is some loss of resolution and some colour rivalry with anaglyph pictures and the method cannot be used when the colour of the display is important’ (1995, p. 26). Accordingly, binocular rivalry with anaglyphs is restricted to contours rather than colours. The separation of the left and right half-images is not complete with anaglyphs: vestiges of the image intended for one eye might be visible to the other, which is referred to as ghosting (Woods & Rourke, 2004). The colour filters are not matched for the light intensities transmitted through them so that matching the monocular images is inferior to that possible with optical stereoscopes (Judge, 1926). In addition, anaglyphic presentation confounds filter transmission differences with eye dominance. As a consequence, anaglyphs have been used sparingly in vision research. Despite these shortcomings, anaglyphs can be used with skill to address complex questions regarding the likely locus of cognitive processing (Antal & de Almeida, 2024; de Almeida et al., 2025).
The situation is otherwise in visual art (Brooks, 2017) and education (Castro-Torres et al., 2020), particularly with presentations on the internet and in virtual reality systems (Qi et al., 2021). Anaglyphs have been embraced in part because they can be displayed to many people at the same time by projection, and the colour filters are compact, inexpensive, and easy to use. The illustrations in this article are anaglyphs which require red/cyan viewers to see the depths and rivalries in their display. It is argued that anaglyphs can be constructed and combined in ways that would be difficult to achieve with other forms of stereoscopy.
In his Foundations of cyclopean perception Julesz (1971) presented computer-generated random-dot stereograms side-by-side so that they could be combined by free viewing. He also presented them as anaglyphs in an Appendix to his book and provided red/green viewers for seeing the depths in them. The patterns for the disparate monocular images can be more complex than computer-generated random-dots. Textured carrier patterns can be based on graphics, photographs or photo-graphics – combinations of photographs and graphic designs or paintings (see Wade, 2023c). Figure 1 is an example of using graphic designs as carrier patterns, whereas Figure 2 starts from a photograph of stones; a disc in depth surrounds portraits of Julesz that are in turn surrounded by the outer rectangle of stones which are in correspondence. With the red/left and cyan/right arrangement the disc of stones appears closer than the larger rectangle surrounding it. Not only does the depth reverse with cyan/left and red/right but the disc also looks larger. In the centre is a double portrait of Julesz, as a younger and older man, and they are presented to different eyes so engage in rivalry. The individual portraits can be seen by viewing through one colour filter alone: The younger man is seen through the red filter and the older, bespectacled Julesz appears through the cyan filter.
Béla Julesz in rivalling age and surrounded by stereoscopic depth by Nicholas Wade. A rivalling double portrait of Julesz in the centre is surrounded by a disc in depth. Viewing with red/left and cyan/right the disc appears closer than the surrounding stones but the disc looks more distant with cyan/left and red/right. A young Julesz can be seen through the red filter alone and the older Julesz can be seen through the cyan filter.
Figure 2 involved the combination of two independently constructed anaglyphs – the stereoscopic disc and the rivalling double portrait. Julesz (1971) introduced the concept of the cyclopean image, the site at which the correspondences and disparities between the monocular images are combined to yield the impression of stereoscopic depth. In one sense, an anaglyphic image, viewed without colour filters, provides a visual analogue of the cyclopean image. Anaglyphs like that shown in Figure 2 can be considered as equivalent to combining cyclopean images.
Constructed stereograms typically contain areas within them that can be seen in depth. As Julesz noted: ‘Such visual displays ordinarily never occur in real-life situations’ (1960, p. 1126). This argument does not have the same force when extended surfaces, rather than enclosed ones, are constructed (see Wade, 2025b), an example of which is shown in Figure 3. The anaglyph appears like a surface with horizontal corrugations, the signs of which reverse with reversal of the red/cyan viewers. The photo-graphic carrier pattern is itself rather complex. The starting point was a digital photograph of a detail within an abstract ‘flow’ painting. The image was digitally modified and combined to form a symmetrical pattern prior to constructing a stereo image. Further digital manipulations of the stereogram followed before reaching the final anaglyph, taking care to retain the critical colour differences necessary for the perception of stereoscopic depth.
Corrugations by Nicholas Wade. With red/left and cyan/right the central horizontal band appears closer, flanked above and below by more distant troughs. They reverse in depth when viewed with cyan/left and red/right so that a horizontal hollow is flanked by two humps.
Figure 3 points to another feature of anaglyphs not shared by optical stereoscopy: they can display the combination of the monocular images which can be viewed without colour filters. The combined views can have an attraction independently of the stereoscopic depth they carry. Thus, it will be argued that anaglyphs can be constructed and combined in ways that would be difficult to achieve with other forms of stereoscopy. The following illustrations indicate some of the ways in which anaglyphs can be combined and manipulated.
Combining Anaglyphs
Anaglyphs themselves can be manipulated and reconstructed to yield novel and often perplexing stereograms. Initially, an anaglyph is made in the standard way, with either enclosed or extended depth features or both. For example, Figure 4 started from a graphical design with a central disc in depth (top). Within each of the other three anaglyphs the upper and lower halves were separated and recombined so that the lower semicircles are in the opposite depth to the upper semicircles. The two middle anaglyphs differ in terms of their alignment with the other half of the circle. In the bottom anaglyph, the lower half of the disc is the negative of the upper half.
Semicircles by Nicholas Wade. With red/left and cyan/right the upper disc encloses a smaller one that appears more distant whereas the two central discs each contain a horizontally bisected smaller one, the upper half of which looks nearer and the lower half more distant. The lower disc is itself bisected with the lower half being the negative of the upper, as is also the case for the apparent depths of the semi-circular areas they enclose. All these relationships reverse with a cyan/left and red/right arrangement of the colour filters.
Photographs of natural textures can also provide a starting point for constructing complex anaglyphs. In the case of Figure 5, a photograph of a wall of ivy leaves was the carrier pattern. It had the characteristics required for carrying disparities, namely, dense but slightly irregular structure. With red/left and cyan/right the whole surface appears to approach on the right side with the right edge looking shorter than the left edge. Two squares can be seen in depth on the slanted surface. They are a duplication of the same anaglyphic square which was independently constructed and has the same disparities which differ from that of the background. They look flat and in depth with respect to the slanting wall in which they are embedded. All these aspects of depth reverse with the arrangement cyan/left and red/right.
Leaf wall by Nicholas Wade. Viewing with red/left and cyan/right the whole pattern appears to be displaced in depth relative to the screen, with the right side looking closer than the left; the depth increases with longer observation as does the apparent size difference between the left and right edges. This is a consequence of the pattern presented to the left eye being horizontally longer than that to the right eye. Two squares can be seen within the leaf wall and they appear more distant. They are duplications of the same square independently derived with flat disparity and they are superimposed on the larger pattern. The enclosed squares appear nearer and the surface of the large leaf wall recedes on the right side with cyan/left and red/right.
At the simplest level, anaglyphs can be combined with one another. Figure 6 consists of six elements, each of which displays a silhouette of a butterfly in depth. In three of the components the stereoscopic butterfly appears closer than the background and in the other three it looks more distant. The background is derived from a photograph of dried autumn leaves on the ground.
Butterflies by Nicholas Wade. A single anaglyph of a butterfly shape in depth with respect to a leaf pattern forms the basis of the figure. It was combined with a left/right reversal of the same pattern so that the butterfly appeared closer in one and more distant in the other relative to the common background. Six butterfly anaglyphs were arranged in alternating depth. With red/left and cyan/right the sequence on the top half is far, near, far and in the bottom half near, far, near. These sequences reverse with cyan/left and red/right.
A constructed anaglyph can be superimposed on itself at different sizes. Figure 7 is based on a photograph of stones on a beach. It was cut in half along a diagonal and that half was placed over the original with a small lateral displacement. This was paired with its symmetrical partner and they made the half-images for the anaglyph. The resulting depth was like an X with the upper and lower triangles at different depths with respect to those on the right and left. The anaglyph was reduced in size four times and superimposed symmetrically on the centre of the original.
Triangulation by Nicholas Wade. The small central square has the characteristics of the original anaglyph. With red/left and cyan/right the upper triangle appears more distant and the lower triangle closer than those on the left and right, both of which are at the same depth.
The leaf theme is continued in Figure 8, which started from a photograph of a beech hedge. An anaglyph was made of a single beech leaf within a pattern derived from the photograph and this was cropped in the shape of the leaf. The left and right leaves have the same sign of disparity which is opposite to that in the central leaf. Thus, the left and right leaves enclose more distant smaller shapes with the enclosed central leaf appearing nearer (with red/left and cyan/right), or the opposite with reversal of the viewers.
Leaves within leaves by Nicholas Wade. Viewing with red/left and cyan/right the enclosed beech leaf shape appears more distant in the left and right leaf outlines and closer in the central figure.
Photographs and graphics can be entwined to create carrier patterns for anaglyphs which in turn can be multiplied and manipulated. They do not need to stay close to the starting image and can be quite complex in construction. The initial elements in Figure 9 are lost in the process of creating the carrier pattern. They were two paintings, one a detail of a tachiste work and the other more geometrical. They were multiplied and modified before the final carrier pattern was produced. The initial anaglyph consists of a bowed surface the centre of which is a large disc surrounding a smaller one at different apparent depths; the bowed depth of the background is of the opposite sign. This anaglyph was combined with itself so that the discs appear in similar curved depth.
Enclosures by Nicholas Wade. Viewing the anaglyph with red/left and cyan/right the central and peripheral regions appear curved towards the observer and two large circular areas to the left and right have the opposite curvature. The circular areas almost meet in the centre and each has a smaller central disc in greater depth.
In addition to combining independently constructed anaglyphs, their combination can be further modified, as in Figure 10. The four quadrants were constructed separately to display different aspects of stereoscopic depth and their amalgamation appears rather like an aerial view of a hilly landscape. The central circular area was extracted from the four combined anaglyphs and the pattern was solarized before restoring the central region in its original state.
Topographical mandala by Nicholas Wade. Each quadrant was constructed independently, with different patterns of disparities and then combined. The resulting anaglyph has differential hills and valleys which emerge with longer inspection. The whole anaglyph was solarized and the original, central circular region was superimposed on it.
Constructed Photographic Anaglyphs
Stereoscopic photographs are typically displayed alone using whatever form of stereoscopy is appropriate. However, in contrast to constructed stereoscopic images, they require appropriate image/eye arrangements to see the stereoscopic depths. For anaglyphs the convention is red/left eye and cyan/right eye; reversing the arrangement to reverse the disparities does not reverse the apparent depth because of the abundant sources of monocular information about the relative depths between structures in the image. An advantage of anaglyphs is that the stereoscopic image itself can be modified in a variety of ways. This is illustrated in Figure 11 which consists of a conventional anaglyphic photograph on the left and a modification of it on the right. A circular region of the stereogram was extracted and replaced in the same position over a solarized monocular component of it. The stereoscopic photographs were not taken with a binocular camera but singly and sequentially with a conventional camera moved laterally between the two exposures.
Sunset on the Blyth Fountain, Newport on Tay by Nicholas Wade. The illustrations need to be viewed with red/left and cyan/right arrangement of the viewers in order to see the stereoscopic depths.
The background that is manipulated can be stereoscopic as well as monocular. Figure 12 is a stereoscopic photograph of a wreck on a beach in the West of Scotland. The depth can be rendered more prominent by isolating a part of the wreck and increasing the contrast to its surroundings, in this case by solarizing the stereoscopic surround.
Diabaig wreck, low tide by Nicholas Wade. View the anaglyph with red/left and cyan/right in order to see the enhanced depth in the central circular region.
Conventional stereoscopic photographs can also be combined with constructed anaglyphs in ways that would be difficult to achieve with reflecting or refracting stereoscopes. Figure 13 presents a central anaglyph of a lily surrounded by a pattern of forsythia leaves which appear in curved depth. The photographs of the lily and the leaves were taken in close proximity because the forsythia tree stands beside the pot in which the lily grows.
Lily and leaves by Nicholas Wade. The central lily is seen in depth with red/left and cyan/right and the background of forsythia leaves appears bowed with the central band further away. The leaf background reverses its apparent curvature with cyan/left and red/right but the lily loses its depth rather than reverses it.
Details of stereoscopic photographs can be extracted from their context and recombined in multiple positions and sizes on a constructed stereoscopic background. An example is shown in Figure 14. The background is derived from a photograph of stones that appears hollow with red/left and cyan/right; stereoscopic photographs of the primate skull were taken in the D’Arcy Thompson Zoology Museum, University of Dundee. Each of the three skulls is derived from the same anaglyph and partially superimposed on one another at different sizes.
Skullduggery by Nicholas Wade. With red/left and cyan/right the depth in the skulls is clear, particularly in the orbit and nasal regions; the stony background appears curved like a shallow grave. The apparent curvature of the stones reverses with cyan/left and red/right but the depth in the skulls is diminished.
It is possible to construct carrier patterns from photographs that do yield depth reversals with colour filter reversals. Indeed, this was the case for Figures 2 and 5 where the subjects (stones and leaves) were selected to provide irregular, dense textures. More conventional photographs can serve a similar purpose. The original photograph for Figure 15 was of a graduation assembly. The photograph was quadruplicated to produce a vertical and horizontal symmetry. An anaglyph consisting of a central circle in depth was formed and then solarized. The disparities are retained through this process but the anaglyph takes on a more abstract impression.
Graduation by Nicholas Wade. With red/left and cyan/right a central circular region stands out in front of the background and it appears beyond the background with cyan/left and red/right.
Rivalling Anaglyphs
Presenting radically different patterns to each eye results in cyclopean competition rather than cooperation; that is, rivalry rather than stereopsis. Rivalry between dissimilar images in each eye was described and devices were made for determining some of its characteristics before stereopsis was examined experimentally (see Wade & Ngo, 2013). The cyclopean competition that produces the dynamic experience of binocular rivalry is not a reflection of alternation between the eyes alone but between pattern elements, too (see Alais & Blake, 2005, 2015; Blake, 2022; Miller, 2013). That is, the experience demonstrates the interaction between local and global features of the stimuli. Thus, in visual science, rivalry has been examined for longer than stereopsis but it has been adopted sparingly by artists (see Wade, 2021b, 2023a). This is surprising because constant variations in perception are provided by the operation of the visual system itself without further intervention of the artist or scientist.
The stimuli favoured by scientists to examine rivalry are orthogonal gratings. They have been widely adopted since Panum (1858) described and illustrated them. He drew attention to the dynamic variations and to the mixtures or composites that are seen and he sought to interpret the phenomenon in physiological terms rather than the psychological factors. Orthogonal gratings are a constituent of Figure 16 which is a combination of two paintings, one geometrical and the other tachiste. The conventional anaglyph made from the half-images was then solarized.
Binocular turbulance by Nicholas Wade. Rivalling anaglyphs do not require a particular colour/eye combination and can be viewed with either red/left and cyan/right or cyan/left and red/right. It might be the case that one combination will result in more even rivalry than the other.
Conventional rivalling anaglyphs can be added to one another, as in Figure 17. Photographs of the same structure (an ornamental metal tree lying against a wall) were taken at different times of the year and made into two anaglyphs by reversing the left and right components. They were then added to one another side-by-side so that each eye alone can see each view, but they engage in rivalry when viewed with both eyes.
Sun and snow by Nicholas Wade. The same pairings are present on the left and right sides, as can be seen by viewing with either red/left and cyan/right or cyan/left and red/right and closing each eye in turn.
The rivalry in Figure 18 is based on a modified detail of a flow painting. The anaglyph was initially made from the same pattern with the half-images at right angles. A central circle was extracted from the anaglyph and then replaced over the negative of the whole anaglyph. The contours flow in alignment from the positive centre to the negative surround, both of which engage in rivalry.
Crossing points by Nicholas Wade.
Stereoscopic and Rivalling Anaglyphs
Examples of anaglyphs containing both stereoscopic and rivalling features have already been presented. Figure 2 is a case in point where a disc in stereoscopic depth with respect to its background has a rivalling portrait at its centre. The stereoscopic and rivalling anaglyphs in this section are drawn from the same starting images. For Figure 19, it is a painted black and white grating crossed by paint streaks in the complementary colour. A photograph of the painting was paired with its orthogonal so that the anaglyph was seen in rivalry. A circular section was extracted and superimposed four times each at 45 degrees to its neighbour; the whole configuration was superimposed on a stereoscopic anaglyph composed from the same original painting.
Gratings in rivalry by Nicholas Wade.
The starting point for Figure 20 was a photograph of Gloriosa Rothschildiana that was modified to create a symmetrical pattern from which a stereoscopic anaglyph was made. A line image was derived from the original design and it was paired with a 90-degree rotated version of itself resulting in a rivalling anaglyph. The centre was extracted and superimposed on the stereoscopic anaglyph.
Gloriosa by Nicholas Wade. The background is in stereoscopic depth and is seen as bowed around the horizontal away from the centre (red/left and cyan/right) or away from the upper and lower edges (cyan/left and red/right); the line patterns in the central disc are in rivalry with both arrangements.
All the components of Figure 21 are derived from the same photograph of a refracting stereoscope after the model introduced by Brewster (see Wade, 1983). The background is formed from line-images of rows of stereoscopes in a frame of the silhouette of the stereoscope. Within the frame the same shape is visible stereoscopically and within that region a smaller shape of the stereoscope is shown in rivalry.
Brewstereoscopes by Nicholas Wade. The stereoscopic stereoscope appears more distant with red/left and cyan/right and closer than the background with cyan/left and red/right while the lines in the smaller central stereoscope pattern engage in rivalry throughout.
Anaglyphic Portraits
A variety of techniques can be applied to the construction of anaglyphic portraits which would be difficult, if not impossible, to construct for reflecting or refracting stereoscopes. This was the case for the portrait of Julesz in Figure 2 and is so for those who follow. Some other examples can be found in Wade (2021a, 2021b, 2023a, 2023b, 2025b).
The material presented in this article is concerned with both the science and art of binocular vision. As such, it is appropriate to conclude with portraits of artists and scientist who have spanned the two areas of enquiry. René Magritte has drawn admiration from artists and has perplexed perceptionists with his paintings. In the perfidy of images, he set words and images in delightful opposition: a pipe shape shared the canvas with painted text stating that it was not a pipe (Foucault, 1983; Wade, 1990). Thus, the message to the viewer is that although this looks like a pipe it is actually pigment on canvas. The pictured pipe cannot be smoked or handled, indeed it seems to be floating in air rather than supported on any surface. Note that Magritte painted the words, too, so he was using one symbolic picture (the written word) to say that another symbolic picture (the shape and colour of the pipe) was not the object represented. When the painted pipe and painted words are in conflict like this we are more likely to think that the pipe-shape does not correspond to the object rather than question the relation of the pipe-word to its referent. Magritte's opposition of word and image expressed the two poles of pictures. Words represent categories of objects whereas spatial images indicate particular instances of them. Despite this disparity both written words and spatial images are pictorial. Both words and images fool the eyes by suggesting closer connections to their referents than exist.
As we know from the vast array of typefaces available, there are many ways in which the letters from the same language can be shaped, and this richness is amplified when hand written letters are included. Letters in idiosyncratic but still recognisable shapes make it possible to play Magritte's discordant tune back to him. By matching the shapes of word and image it could be said that the conflict between them has been removed. Figure 22 plays further variations on this tune by introducing stereoscopic effects. Two anaglyphs are juxtaposed, both using the same half-images but transposing the eyes to which they are presented. Both contain a portrait of Magritte in one eye combined with his pipe picture. The other eye has a variant of my graphical response to Magritte, with the letters UNE PIPE reflecting the shape of his pipe placed above the statement that it is a pipe; its title is The integrity of words (see Wade, 1985, Figure 1). The two messages can be seen in isolation with either eye alone but they engage in rivalry when viewed with red/cyan filters. Ambiguity is alluded to with the two small silhouette pipes spanning the two halves; the orientational ambiguity of the pipe stems seen with a single eye is resolved stereoscopically.
Images of Magritte by Nicholas Wade.
Maurits Cornelis Escher similarly capitalised on the paradoxes of pictures (Bool et al., 1982). His forte was to create representations of spaces that would be impossible to construct. His drawings and prints represent ambiguous or impossible worlds that can only exist on paper: fish define fowl and devils provide the outlines for angels, often with one shape metamorphosing into others (see Ernst, 2007). Artists and architects have been fascinated by Escher's distortions of perspective, and mathematicians and physicists have been intrigued by his geometrical manipulations of repetitive patterns. He made many ingenious modifications of the ‘impossible’ triangle, introduced by Oscar Reutersvärd in 1934 (see Mortensen, 2022). His figure consisted of outlines of stacked cubes, each line of which was consistent, but the connections between them were contradictory. It would not be possible to stack nine boxes in the way they have been drawn. Reutersvärd stumbled across the design almost by chance. He made a drawing of six cubes corresponding to those forming the central star and then was startled when he added the three corner cubes thereby creating the ‘impossibility’. The ‘impossible’ triangle is also referred to as the Penrose triangle, after Roger Penrose and his father, Lionel (Penrose & Penrose, 1958). Penrose and Escher were not aware of Reutersvärd's earlier examples until some years later. Since that time, artists and scientists have tried to construct such ‘impossible’ figures in three dimensions, and some of the objects are called ‘Meschers’ (Dodik et al., 2025)!
It is possible to use letter shapes to make similar pictures; an example using the letters spelling Escher's full name can be found in Wade (1985, Figure 41) and is modified in Figure 23. Embedded triangles defined by the letters of his name appear to have opposing perspective impossibilities and the inner ones contain a portrait of Escher. An anaglyph of the design was constructed so that the pictorial perspective is either enhanced or opposed by the disparities, depending on the arrangement of the viewing filters. The anaglyph was then placed on a double portrait of Escher in a simple tile patterns (see Wade, 2015). Escher's symmetrical tessellations were influenced by Arabic decorative tiles. He subsequently produced graphical designs involving repetitive elements that often varied in size or orientation. The same self-portrait of Escher is in the tessellations and the triangles.
Impossible Maurits Cornelis Escher by Nicholas Wade.
Hermann Helmholtz played an important role in the development of stereoscopy, and stereoscopic phenomena were used by him to support his inferential theory of vision (Cahan, 1993; Turner, 1994). He introduced the telestereoscope to enhance disparities for distant objects (Helmholtz, 1857). He also wrote about separating images to the eyes by colour (anaglyphs) as had been described by Rollmann (1853). They were mentioned in the Handbuch: ‘He [Rollmann] draws two projections on the same black card, one with red lines, the other with blue. Then he takes a red glass in front of one eye and a blue glass in front of the other and only sees the red lines with that eye, with this only the blue ones, which can then be combined to form a relief’ (translated from Helmholtz, 1867, p. 685). That is, the red lines are seen as black through the blue glass as are the blue lines through the red glass. Surprisingly, this text was incorrectly translated by Southall who wrote ‘…he can see only the red lines through the red glass and the blue lines through the blue glass’ (Helmholtz, 1925, p. 356).
Helmholtz (1873, 1881) gave many popular lectures, one of which was ‘On the relation of optics to painting’. The section on ‘form’ deals with the paradox of painting – creating the appearance of depth on a flat surface that can be clearly perceived as such. He described the perspectival perception for a single eye and went on to consider binocular viewing: ‘We however see the world with two eyes, which occupy somewhat different positions in space, and which therefore show two different perspective views of objects before us. This difference of the images of the two eyes forms one of the most important means of estimating the distance of objects from our eye, and of estimating depth, and this is what is wanting to the painter, or even turns against him; since in binocular vision the picture distinctly forces itself on our perception as a plane surface’ (Helmholtz, 1881, p. 80). Helmholtz points clearly to the conflict between the flatness of the canvas as seen with two eyes and the apparent perspectival depth within it. Moreover, he draws a geometrical parallel between disparities with two eyes and those of motion parallax due to lateral movements of one eye alone: ‘For it must be observed that as we use different pictures seen with the two eyes for the perception of depth, in like manner as the body moves from one place to another, the pictures seen by the same eye serve for the same purpose’ (Helmholtz, 1881, p. 81).
Several portraits of Helmholtz are combined in Figure 24. In the centre is a double portrait showing a young man (from a daguerreotype in 1848) and an older man (from a lithograph in 1876). The background is derived from a photograph of his statue that stands in front of the entrance to the Humboldt University, Berlin. In Figure 24 the photograph has been multiplied to form the two rows of overlapping statues of Helmholtz, but with opposite disparities in the upper and lower rows. Flanking the rows are halves of an anaglyph of the statue. Thus, Figure 24 is the combination of four independently produced anaglyphs. More anaglyphs of Helmholtz can be found in Wade (2021c).
Helmholtz's stature by Nicholas Wade.
It is appropriate to finish with an anaglyphic tribute to Charles Wheatstone, the inventor of reflecting and refracting stereoscopes (see Pellerin & May, 2021; Wade, 1983). It is rarely the case that an inventor of an instrument to advance the investigations of vision addresses so many fundamental questions regarding the phenomena it uncovers. Wheatstone established that viewing dissimilar pictures results in the appearance of depth, and he conducted a series of systematic manipulations of the figures in order to discover the nature of the relationship. He demonstrated that the sign of disparity (crossed or uncrossed) determined the relative depth seen (nearer or farther), that there was a limit to the disparity yielding singleness of vision, that eye movements were not involved (because depth was seen in disparate afterimages), and that radically different pictures or colours resulted in binocular rivalry. He also introduced abstract (dot) stereograms (Wade, 2025a). His influence on Helmholtz was profound and acknowledged in the Handbuch (Helmholtz, 1867).
Although Wheatstone's initial artistic interests were in audition, it was through photography that his impact on visual art was most keenly felt. He was a friend of Talbot, who announced his photographic discoveries in January, 1839, months after Wheatstone presented his stereoscope to the public (see Pellerin & May, 2021). Thereafter the arts of stereoscopy and photography were closely bound. Talbot directed Wheatstone to make the first stereoscopic photographs but the disparities were too large and their combination resulted in rivalry (see Klooswijk, 1991; Wade, 2021b). The anaglyphic tribute to Wheatstone involves both rivalry and stereoscopic depth. The 150th anniversary of Wheatstone's death was in 2025 and it is marked in Figure 25. Three rivalling portraits of Wheatstone, as a younger and older man, are differentially masked by the numbers marking the anniversary; each is surrounded by a pattern of stones a disc of which is in stereoscopic depth. The three large circles are surrounded by a pattern of wheat which is also modulated in depth.
Wheatstone's anaglyphic anniversary by Nicholas Wade.
Discussion
Historically, anaglyphs have tended to act as inferior substitutes for reflecting and refracting stereoscopes. The optical separations of the half-images to each eye are not as discrete and the colours of the originals are not retained. Despite these shortcomings, anaglyphs are growing in popularity. Among the reasons for this are that the colour filters are inexpensive and the anaglyphs can be printed or presented on screens to be seen by many. This applies increasingly to digitally transmitted anaglyphs because the original colours in the anaglyphs can be retained more precisely than when they are printed. An under-explored advantage of anaglyphs is that they afford a wider range of graphical manipulations than is available to other forms of stereoscopic presentation. Mirror and prism stereoscopes, autostereograms, cross-polarization and rapid image/eye alternations do not afford either the post-stereoscopic or combinational possibilities of investigating binocular cooperation and competition open to anaglyphs. In addition, they do not offer the opportunity of seeing the combined half-images non-stereoscopically. An impression of the stages through which the process can pass from the start to the final anaglyph is shown in Figure 26.
A summary of the stages in the construction of Corrugations (Figure 3). a, digital photograph of part of an abstract painting which was b quadruplicated to form a pattern with vertical and horizontal symmetry; c, the half-images combined by StereoPhoto Maker to make the anaglyph d; the brightness and contrast of the anaglyph were adjusted e after which it was solarized f; the brightness and contrast were adjusted again to produce the final anaglyph g.
The final anaglyph in Figure 26 is Corrugations (Figure 3 of this article) and it is a simple construction relative to those that follow because it has a single starting image and it is not combined with any other independently constructed anaglyphs. Optical stereoscopes could not proceed beyond c in Figure 26. That is, they can present the half-images to the left and right eyes prior to the cortical combination resulting in stereoscopic depth perception. Of course, the colours would have been retained rather than modified, as is the case with anaglyphs.
Only one image in this article (Figure 11, left) is what can be called a conventional anaglyph stereogram. That is, it consists of the combination of two photographs taken with small lateral separations. It could have been presented in Universal Freeview format. This does not apply to any of the other anaglyphs which are either combinations of independently constructed and cropped stereograms or involve graphical manipulations of the stereogram(s) to make the final anaglyph (post-processing). In principle, all the stereograms could be deconstructed and presented in reflecting or refracting stereoscopes but this is not straightforward even for conventional anaglyph stereograms (Kunze et al., 2020; Yan et al., 2025). The situation is much more challenging when dealing with stereograms combined from independently constructed anaglyphs and/or those that have involved post-processing. It is not possible to present them in Universal Freeview mode because there are no simple monocular half-images that could be viewed. This article draws attention to some of these anaglyphic manipulations and it is hoped that it might encourage others to extend them further.
Conclusions
The illustrations displayed are based on scientific considerations but expressed in the graphical language of art; they are intentionally an attempt to bridge the gap between the science and art of stereoscopy. All the stereograms shown in this article are presented as anaglyphs. As such, there are left and right eye images, distinguished from one another by colour and contour. The point of interest, however, is that they could not have been constructed for other types of stereoscopic viewing. The allure of anaglyphs is based on the opportunities they offer to explore new worlds of three-dimensional space. It is as if they provide the possibility of manipulating the equivalents of cyclopean images.
Footnotes
Author Contribution(s)
Funding
The author received no financial support for the research, authorship, and/or publication of this article.
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.