The Mainz-Linez Illusion

Abstract

This paper introduces the Mainz-Linez Illusion (MLI), a novel dynamic display in which rectilinearly moving targets appear to deviate from their true physical paths and instead give the impression of following the curves of static background elements. We attempt to relate the MLI to previously known effects and discuss possible mechanisms. We particularly focus on the possible role of negative afterimages, and speculate how their emergence and interaction with physical contours might contribute to some of the unique characteristics of the MLI. We also provide an online demo where readers can experience the effect and manipulate relevant parameters for themselves.

How to Cite this Article

Thornton, I. M., Riga, A., Zdravković, S., & Todorović, D. (2025). The Mainz-Linez Illusion. i-Perception, 16(6), 1–6. https://doi.org/10.1177/20416695251399121

This paper introduces the ‘Mainz-Linez Illusion’ (MLI; Movie 1), which we created to help celebrate ECVP 2025, held in Mainz, Germany (https://ecvp.eu). While the red target discs move vertically, they give the strong illusory impression of following the curves of their respective static white lines. To experience the illusion, keep your eyes steady on any of the small black fixation dots. Directly tracking a red disc is an easy way to experience its veridical straight path. Note that the illusion does not require multiple items. We include them here to boost the overall visual impact of the display. Targets and lines can be removed in the interactive demo that provides full control over all parameters at https://maltacogsci.org/MLI/. See the OSF page for source code and downloadable movies https://osf.io/vwfnd/.

The MLI evolved from our work with the rocking line illusion (RLI; Thornton & Todorović, 2023) and the furrow illusion (Anstis, 2012; Riga et al., 2025; Thornton & Riga, 2024), both of which also involve the misperception of motion direction when translating targets interact with static inducing elements. There are, of course, many other closely related effects, and we provide chronology as an online table that can be accessed at https://maltacogsci.org/MLI/MLI_Table1.html or via the OSF page.

However, what makes the MLI potentially interesting are not similarities to these previous phenomena, but rather what appear to be systematic differences. For example, in the RLI, targets also appear to wave or rock when they move in the context of inducing lines, but this only occurs when the target/inducer intersections are relatively small (< 1°). Fixation is not required, and indeed the illusion is enhanced when the target is tracked. The MLI, in contrast, can be observed with large or small elements – try stepping back from the screen – but critically does require steady fixation. Importantly, fixation can be either at the very centre of the display, or in the periphery.

The presence of illusory displacement with central fixation distinguishes the MLI from many other related illusions. The furrow illusion, for example, is absent in central vision, and its occurrence/amplification with peripheral viewing has played a major role in conceptions about underlying mechanisms. Specifically, it is thought that without the aid of central vision, the motion of extrinsic intersections becomes erroneously combined with the true motion of the target, shifting perceived heading (e.g., Anstis, 2012; Cormack et al., 1992; Riga et al., 2025).

So why does the MLI persist with central viewing? One important factor might be the presence of negative afterimages. Elsewhere, we have noted that maintaining steady fixation in these types of displays leads to the rapid formation and release of negative afterimages (Riga et al., 2025; Thornton & Riga, 2024). As a target occludes a background element, it dynamically releases a negative copy of the contour, presenting the visual system with a new signal. In Movie 1, such negative afterimages appear as dark grey line segments within each target. To isolate and amplify these afterimages, Movie 2 shows a variant where the target and the wider background are the same shade of grey. Although there are physically only two contrast levels in this display (the white target + middle grey), a moment's fixation will suggest otherwise.

How might negative afterimages contribute to the MLI and help explain its occurrence with central viewing? One possibility is that dynamic afterimages simply enhance or more strongly bind the same intersection motion thought to contribute to effects such as the furrow illusion (e.g., Anstis, 2012; Cormack et al., 1992; Riga et al., 2025). In the MLI with circular targets, such intersections form deletion/accretion boundaries that follow the leading/trailing edge of the target, moving along the static background contours themselves. As the afterimages give rise to additional negative contrast boundaries at these same points, the salience of the intersection motion could be enhanced, even to the point where it can be erroneously combined during central viewing.

Afterimages could also contribute to the MLI independently of intersection motion. For example, as the negative afterimage of the curve emerges, it could be viewed as an additional feature within the target. In terms of static snapshots, such a feature might appear to dissect the target asymmetrically, affecting its ‘balance’ and possibly perceived position. As a dynamic feature, the orthogonal motion of the afterimage within the target – relative to its veridical path – could give rise to some form of induced motion (Duncker, 1929). That is, the integration of such feature motion with the overall path motion could bias the perceived position of the target via flow parsing (Falconbridge et al., 2022; Warren & Rushton, 2009), vector decomposition (Johansson, 1950) or some other reference frame mechanism. Inspired by the ‘negative lens’ stimuli of Anstis (2012), we provide an online demo where readers can further explore how ‘optimal’ afterimages might behave as internal object features. Further details on the OSF page, and at https://maltacogsci.org/MLI/MLI_NegativeLens.html.

We are clearly still in the first stages of exploring these ideas. We can, however, offer some preliminary observations that suggest the MLI is independently influenced by intersections and afterimages. Furthermore, we suggest that switching between central and peripheral viewing can be used to modulate their influence. In the interest of space, we simply list these observations here, but we hope to explore them further in later work. For now, the main MLI demo can be used to verify each observation.

First, we note an asymmetry in target contrast behaviour. Setting target grey-level so that it reduces the saliency of afterimages (given a specific line colour), will reduce or eliminate illusory motion with central viewing, but have less effect on peripheral viewing. For example, with white lines and default background (#808080), afterimages appear dark grey. Decrement target grey (e.g., #656565) reduces the saliency of the afterimages and the central illusion. With black lines, the lighter afterimages can be similarly masked with increment target greys (e.g., #959595). Second, placing the targets behind the lines (and thus eliminating afterimages) removes the central illusion, but gives residual effects with peripheral viewing. Third, introducing moving fixation breaks the illusion when tracking centrally, but only reduces it when tracking peripherally. Movie 3 allows you to test this latter observation for yourself. Note that when the targets become grey, there is a clear change in (amodal) appearance when tracking in central and peripheral vision, which may prove informative.

So far, we have only mentioned two mechanisms: Afterimages and intersections. Another line of inquiry concerns the influence of static contrast gradients between the edges of the curves and the wider surround (see Todorović, 2021 for review). Recently, we suggested that the RLI may be a side-effect of moving a target across such boundaries (Thornton & Todorović, 2023) and it remains possible that such factors also play a role here.

To conclude, we have presented a novel display which provides a very compelling impression of illusory direction change and have speculated about possible mechanisms. We invite readers to continue exploring the MLI via the online demo and we hope that such exploration will lead to further insights and observations.