Why does the rotating snake illusion work

Recently, we found certain gray-value conditions where a weak illusory motion occurs in the opposite direction. Of the four models for explaining the illusion, one also explains the unexpected perceived opposite direction. We here present a simple new model, without free parameters, based on an array of standard correlation-type motion detectors with a subsequent nonlinearity e. The model predicts a the pattern-appearance motion illusion for steady fixation, b an illusion under the real-world situation of saccades across or near the pattern pattern shift , c a relative maximum of illusory motion for the same gray values where it is found psychophysically, and d the opposite illusion for certain luminance values.

Certain spatial patterns can evoke illusory movement, especially under dynamic viewing. While usually rendered in color, it is nearly just as strong in gray Conway et al. The Rotating Snakes Illusion with its many variations continues to fascinate beyond the vision research community. Furthermore, in the natural viewing situation, the Snake pattern does not suddenly appear from neutral background, as assumed in this model, and for seeing the illusion, saccades are necessary small or large; Otero-Millan et al.

This, together with saccades while viewing, or the appearance of the pattern out of a gray background, predicts the standard Rotating Snakes Illusion, including the parameter region leading to the opposite direction of rotation. These findings suggest that the Rotating Snakes Illusion can be regarded as a necessary side effect when arrays of motion detectors are combined in a nonlinear fashion. We will present the model in two steps, beginning with a simpler situation, namely, that of pattern appearance of the stimulus from a gray background.

We will then move on to treat natural viewing conditions, namely, that the observer performs saccades across the stimulus picture. In the model presented here, it proved necessary to add a sign-conserving nonlinearity of nearly any shape, see later at the output of individual motion detectors, before summing across the detector array. We tested various sigmoid functions that all share the property of being rotationally symmetric around zero, including the arc tangent, hyperbolic tangent, and logistic function.

This first approximation to a working model is based on the observation that the appearance of a Snake Pattern from a gray background pattern appearance evokes a strong apparent motion even with steady fixation. To make the geometry more tractable, we uncoiled the original Rotating Snakes Illusion with its several Snake wheels , and investigated a pattern consisting of repeated Snake cycles , each cycle containing four gray values Figure 1B.

B: Two sample cycles of a Snakes sequence Murakami et al. The output of each individual motion detector passes a nonlinear transfer function, before being summed across the array of motion detectors, yielding a net motion output. The spatial span of each detector R equals the width of one stripe of the Snake pattern, and there is no space between adjacent detectors.

We use the sign convention that a dark structure on light background yields a positive output when moving to the right. Top: three different transfer functions a, linear; b, tangent; c, arc tangent.

A: With a linear transfer function, no net motion signal appears. B: We tested a range of saturating nonlinearities and in all cases there appears a net motion signal for any off-diagonal i.

C: Accelerating nonlinearities also lead to a net motion output, with an inverted sign direction of apparent motion compared to saturating nonlinearities.

Main assumption : The sum or the average, these differ here only by a scaling factor of an array of such motion detectors, stimulated by the appearance of a Snake cycle, subserves the apparent motion Figure 1B.

Thus, given. In this generality, we could not solve the problem analytically, so implemented it as a computational model in the R language R Core Team, , a free open-source programming and statistical environment, and graphs were produced using the package ggplot2. Full source code in the repository; Bach, a. Nonzero model outputs only occurred with the insertion of the aforementioned nonlinearity. Model, First Approximation. A: On top, a sequence of gray squares turns into the Snake sequence below.

That sequence is the input to an array of motion detectors cf. Figure 2B shows the net motion for the full parameter space of the possible gray values g 1 , g 2.

The various shapes of the nonlinearity affected the magnitude of the net motion output, but the distribution in g 1 , g 2 space remained the same for all the tested nonlinearities. Nonlinearities within the receptors themselves were tested as well, but had no qualitative effect in this model and were thus omitted from further analysis, although physiologically they are likely to occur.

We model the effects of saccades across the image by stimulating the motion detector array with Snake cycles changing their positions randomly Figure 3. Assuming that the latter average out, we will only compute the effects of lateral shifts here.

The simplification of the previous figure pattern appearance: snakes appearing from gray is now made more realistic: snakes appearing from all possible horizontal shifts of a previous snake pattern. The shift shown for half a cell width is but one example of the possible shifts. In Figure 3 , we sketch the model structure: As an initial condition, a Snakes sequence could have any possible shift relative to the final position which is equal to the position of the detectors R i.

Since the problem is circular, we averaged over 40 small shifts of the Snakes sequence until it was identical again. The results are shown in Figure 4 using three different transfer functions. Unsurprisingly, no motion illusion appears for a linear transfer function A. Figure 4C adds an accelerating nonlinearity: illusory motion appears again, but with opposite sign; the same sign reversal occurs also in the pattern-appearance model not depicted.

For all tested nonlinearities, we found areas in the g 1 , g 2 plane which give nonzero results and thus illusory motion , but the relative areas of positive and negative motion varied slightly. It is one of a class of peripheral drift illusions; whatever part of the figure is in the centre of our visual field appears motionless as indeed it is , while the parts seen in our peripheral vision appear to move.

No-one is quite sure as to how the Rotating Snakes illusion works, although there is some consensus that it involves a difference in the processing latency of signals corresponding to different parts of the figure. Conway et al. The illusory motion is then explained as an example of the reverse phi phenomenon first described in Anstis and Rogers : a bright spot appearing and fading at some point in the visual field, subsequently followed by a dark spot appearing and fading at some other point, will create a sense of motion from the dark stimulus toward the light stimulus if this pattern is cycled.

If the reverse phi phenomenon explains illusory motion, the reversing patterns explain why some snakes rotate clockwise and others anticlockwise. A processing latency mechanism is consistent with the fact that the illusion ceases when our gaze is fixed, because in that case the signal from each part of the visual field is fairly constant.

The Rotating Snakes Illusion is also interesting because it is relevant to debates about modularity, cognitive penetration, and the nature of experience. To explain: on the hypothesis that the mind is modular, a mental module is a kind of semi-independent department of the mind which deals with particular types of inputs, and gives particular types of outputs, and whose inner workings are not accessible to the conscious awareness of the person — all one can get access to are the relevant outputs.

For a general discussion of cognitive penetration, see Macpherson Philosophers have also been interested in what illusions like the Rotating Snakes Illusion can tell us about the nature of experience. For example, in the case of experiencing the Rotating Snakes Illusion, it would seem to be that the one can know that nothing on the screen rotates whilst at the same time experiences rotating snakes.

If so, then this might count against the claim the perceptual states are belief-like, because if perceptual states were belief like then, when experiencing the Rotating Snakes Illusion one would simultaneously believe that the snakes were, and were not, rotating.

This would seem to entail that one was being irrational, because one would simultaneously be holding contradictory beliefs. But it seems highly implausible that one is being irrational when under going this illusion.

Antis, S. Conway, B. Neurosci 25, Faubert, J. Fraser, A. Do not become alarmed. For one, the effect depends on eye movements, and these are known to differ markedly between subjects without relating in a clear-cut way to psychological traits.

After my comments above, this fact check by USA Today arrived at same conclusion. Kitaoka A, Ashida H Phenomenal characteristics of the peripheral drift illusion.