Illusory Spirals: When the Brain Curves What Is Straight

The Fraser spiral appears to wind toward the center.

Yet every major band closes onto itself.

The image contains concentric circles.

The spiral exists in perception, not in the coordinates.

Other static images seem to rotate, slide or breathe.

These effects reveal that vision is not passive recording.

The retina receives local contrast, partial contours and retinal motion.

The visual system estimates global shape, direction and stability.

An illusion occurs when an artificial pattern drives a normally useful perceptual computation toward a result that differs from the physical stimulus.

Distinguish:

• file geometry;
• retinal image;
• perceived shape.

The file specifies exact circles, segments and luminances.

The retinal image depends on size, optics, eccentricity and eye movements.

The percept may contain curvature, tilt or rotation.

The difference can be measured by adding an opposite physical distortion until the pattern looks neutral.

Shape illusions alter perceived orientation or curvature:

• Fraser;
• Zöllner;
• Café Wall.

Motion illusions add perceived velocity:

• Rotating Snakes;
• Fraser-Wilcox;
• Enigma;
• Ouchi;
• Pinna-Brelstaff during radial motion.

One display may combine both.

Fraser’s 1908 twisted-cord illusion uses concentric rings built from oblique local elements. ^[1]

The local orientations differ from the true circle tangent.

Global integration produces a continuously deviating contour.

Because the pattern wraps around a center, the deviation appears spiral.

Tracing or recoloring one ring reveals closure.

Let the true contour tangent be:

$\theta_{c}$

and local element orientation be:

$\theta_e=\theta_c+\delta$

A pedagogical mixture is:

$\theta_{\mathrm{perceived}}=(1-w)\theta_c+w\theta_e$

so:

$\theta_{\mathrm{perceived}}=\theta_c+w\delta$

This is not a complete neural model.

It demonstrates how a repeated local bias can accumulate into a global spiral percept.

The interactive display should vary:

• local tilt;
• ring width;
• contrast;
• background;
• spatial frequency.

A compensating physical spiral:

$r(\theta)=r_0+b\theta$

can be adjusted until the rings appear circular.

The fitted b is a local, nonclinical estimate of illusion strength.

Yun and colleagues compared physical circles and spirals with parallel or twisted cords. ^[2]

Twisted cords could make circles look spiral and physical spirals look more circular.

The result shows a competition between global contour and internal orientation.

Long parallel lines crossed by short oblique inducers appear nonparallel.

The effect depends on inducer angle, spacing, contrast and spatial scale.

Orientation interactions, grouping and depth context have all been investigated.

No single sentence should be presented as a complete explanation.

Staggered dark and light tiles separated by intermediate mortar make parallel lines appear tilted.

Local contrast boundaries generate wedge-like orientation signals at certain spatial scales.

Mortar luminance strongly changes the effect.

Kitaoka, Pinna and Brelstaff showed that several tilt illusions produce spiral illusions when arranged as concentric rings.

A small tangential error repeated around a center becomes a global spiral percept.

Early visual signals are local.

A spiral is global.

The brain integrates orientation, scale, position and continuity over large regions.

The illusion appears when local cues bias the global solution.

Primary visual cortex contains neurons selective for edge orientation. ^[3]

Fraser patterns activate signals for both the circular contour and oblique internal elements.

Perception results from population activity and interaction across levels, not one detector.

High spatial frequencies represent fine segments.

Lower frequencies represent broad envelopes.

Blurring Café Wall reveals diagonal structure.

Changing scale in Fraser changes the balance between cord and carrier contour.

A software blur is only an analogy to biological filtering.

Proximity, similarity, continuation and closure influence grouping.

Oblique segments may be grouped along an implied direction.

Gestalt principles describe perceptual regularities but are not a complete physiological account.

A local detector viewing an edge can measure only motion normal to the edge.

Tangential motion remains ambiguous.

Global motion requires integration across orientations.

This principle is central to Pinna-Brelstaff.

Rings made of tilted elements rotate perceptually when the image expands or contracts.

The real motion is radial.

The perceived relative motion is tangential.

Reversing element orientation reverses the perceived rotation.

Static motion illusions often use asymmetric luminance units.

A repeated sequence such as:

black → dark gray → white → light gray

may produce different response timing across neighboring elements.

The spatial order then resembles a temporal motion sequence.

Rotating Snakes is physically stationary but often appears to rotate.

The effect is influenced by:

• luminance order;
• contrast;
• peripheral viewing;
• fixation changes;
• blinks;
• spatial scale.

Susceptibility varies.

A simplified response is:

$R_i(t)=A_i\left[1-\exp\left(-\frac{t}{\tau_i}\right)\right]$

Differences in tau across neighboring elements can create an apparent motion signal.

Real visual responses are more complex than this illustration.

The effect is often stronger away from direct fixation.

Peripheral receptive fields are larger and spatial-temporal integration differs from the fovea.

The stimulus must be scaled appropriately.

Fixation contains microsaccades, drift, tremor and blinks. ^[4]

These transients move or reset the retinal image.

Studies have reported relationships between eye transients and reported illusory rotation.

They are contributors, not a universally complete explanation.

V1 supplies local direction signals.

MT+ integrates motion over larger regions.

Neurophysiology and fMRI show that static motion illusions recruit ordinary motion-processing networks.

Activation does not by itself prove a single causal origin.

Illusion strength varies with age, fixation, contrast sensitivity, scale, lighting and display.

A weak or absent effect is not a diagnosis.

Enigma produces apparent flow in radial textures.

Ouchi produces relative sliding between center and surround under small retinal motion.

These examples show that “illusory motion” includes multiple computational problems.

After viewing real motion, a stationary scene may move in the opposite direction.

This adaptation effect differs from direct anomalous motion in a static pattern.

Methods include:

• forced choice;
• rating;
• adjustment;
• motion cancellation;
• adaptive staircase.

A simple web experiment may estimate:

$\omega_{\mathrm{illusion}}\text{ approximately equals }-\omega_{\mathrm{cancellation}}$

but it is not a clinical or published measurement.

Illusions allow controlled perturbation of:

• luminance;
• orientation;
• eye movement;
• context;
• scale;
• attention.

They reveal dependencies that ordinary scenes hide.

Artificial models may reproduce some illusion-like outputs.

That does not imply shared mechanisms.

Models can also fail on human illusions or report illusions where humans see none.

A 2026 preprint found that most tested optical-flow models failed to produce human-like Rotating Snakes flow, while one human-inspired dual-channel model produced the expected direction under simulated saccades.

This must be labeled emerging research.

The article should include:

1. Fraser Lab; 2. Tilt-to-Spiral converter; 3. Pinna-Brelstaff vector explorer; 4. Rotating Snakes luminance lab; 5. eye-transient simulator; 6. psychophysical motion cancellation; 7. human-versus-model comparison.

The Fraser spiral is not physically present.

That is the point.

Local orientations, circular organization and global integration create a spiral percept.

In Rotating Snakes, static rings also appear to move.

Perceived form is not always measured form.

Perceived dynamics is not always physical motion.

Illusory spirals separate stimulus from percept.

They reveal orientation filtering, global integration, temporal response, eye movements and motion processing.

Different illusions use different combinations of these mechanisms.

Vision is an active estimate of the causes of retinal signals.

The spiral appears in that estimate.