Parametric Visual Stimuli for an Intra-/Extradimensional Set-Shifting Task

Overall assessment

Your two proposed approaches are both viable, but they serve slightly different purposes:

• Quaddles are already a reasonably validated multidimensional object space, with explicitly controllable 3-D parts and surface properties.
• Brain Explorer–style microorganisms offer much tighter experimental control, faster rendering, easier generation of thousands of exemplars, and cleaner separation between dimensions.

For a relatively faithful CANTAB-style IED task, I would make the procedurally generated microorganism family the primary stimulus set, while using Quaddles or another 3-D set as a secondary generalisation set.

The crucial point is that the generator should create many novel exemplars within each perceptual dimension, rather than merely producing many combinations of a small number of familiar objects. In the CANTAB IED, simple one-dimensional discriminations are followed by compound stimuli, intradimensional shifts introduce new exemplars while preserving the relevant dimension, and the extradimensional shift makes the previously irrelevant dimension relevant. The standard implementation contains nine stages, including two steps in which the second dimension is first introduced separately and then combined with the first. [1]

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1. Alternative parametric stimulus families

1. Procedural “microorganism” or “alien cell” objects

This is essentially a formalised and improved version of the Brain Explorer approach.

A single object could have four independent dimensions:

Dimension	Possible parameters
Outer contour	radial frequency, modulation amplitude, aspect ratio, symmetry, smoothness
Appendages	length, curvature, orientation, tip type, thickness
Surface texture	spots, stripes, Voronoi cells, waves, noise scale
Colour/material	hue, chroma, brightness, gradient direction

The outer contour can be defined mathematically as:

[ r(\theta)=R\left[1+\sum_{k=1}^{K} a_k\cos(f_k\theta+\phi_k)\right] ]

where:

• (R) controls overall size;
• (f_k) controls the number of lobes;
• (a_k) controls their prominence;
• (\phi_k) rotates the contour structure.

This is related to radial-frequency and Fourier-descriptor stimulus spaces, both of which have been used to create controlled closed contours in vision research. Radial-frequency patterns are generated by modulating the radius of a circle, while Fourier descriptors provide a more general representation of closed outlines. [2]

Advantages

• Very easy to make thousands of unique exemplars.
• Dimensions can be independently switched on and off.
• Can be rendered directly as SVG, PNG or Psychtoolbox textures.
• No uncontrolled lighting or viewpoint variation.
• Well suited to touchscreen testing.
• Easy to equalise object area, luminance and contrast.
• Can be visually engaging without resembling familiar objects.

Main limitation

Some mathematical shape parameters are not perceptually independent. For example, increasing lobe amplitude may also increase perimeter, edge density and apparent size. This can be handled by normalising the generated contour and empirically matching discriminability.

My rating for IED use: 5/5.

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2. RUBubbles

RUBubbles are published artificial category stimuli consisting of coloured spheres arranged in 3-D space. Their MATLAB generator independently controls variables including:

• sphere number;
• sphere size;
• sphere colour;
• sphere position;
• spatial configuration.

They were explicitly developed for category-learning studies, including generating exemplars as distortions around category prototypes. [3]

Suitable IED dimensions

You could define:

• Dimension A: sphere size;
• Dimension B: colour;
• Dimension C: arrangement or configuration;
• Dimension D: number of spheres.

Advantages

• Existing MATLAB implementation.
• Large multidimensional space.
• Objects look coherent and three-dimensional.
• Configuration can vary continuously.
• Category prototypes and controlled distortions are straightforward.

Limitations

• Sphere number is partly a numerosity dimension.
• Sphere position changes occlusion, occupied area and apparent density.
• Configuration may be processed holistically rather than as an independently selectable feature.
• Perspective and shading must remain fixed.

RUBubbles would be particularly useful if you want a halfway point between simple 2-D blobs and full Quaddles.

My rating for IED use: 4/5.

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3. Fribbles

Fribbles are multipart novel objects organised into species or body classes, with multiple interchangeable components attached at defined positions. They have been used extensively in object recognition, category learning and neuropsychological research. [4]

A Fribble-like generator could independently vary:

• central body;
• upper appendage;
• lower appendage;
• tail or terminal part;
• colour or texture.

Advantages

• Dimensions correspond to identifiable object parts.
• Very natural for testing attention to one part while ignoring another.
• Allows categorical as well as metric dimensions.
• Easy to construct new objects by recombining parts.

Limitations

Published work has noted that the available parts are not necessarily equally discriminable, and some positions may attract more attention than others. Fribbles can also encourage a local part-comparison strategy instead of attentional selection between abstract dimensions. [4]

A custom “micro-Fribble” system with two or three attachment sites would be better than using the original Fribbles unchanged.

My rating for IED use: 3.5/5.

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4. Geon or superquadric assemblies

Another option is to assemble objects from simple parametric solids:

• spheres;
• cylinders;
• cones;
• rounded cubes;
• tapered prisms;
• bent tubes;
• superellipsoids.

Possible dimensions include:

• part shape;
• part number;
• part arrangement;
• relative part size;
• surface texture;
• colour.

A body might consist of one central superellipsoid plus two attached parts. New exemplars can then be produced by changing the body curvature or replacing the attached geons.

Advantages

• Extremely easy to generate in Blender, Unity, Three.js or MATLAB.
• Object structure remains interpretable.
• Continuous morphs can be made between spheres, cubes, cylinders and tapered forms.
• Easier to control than Greebles or realistic objects.

Limitations

Part identity and configuration may interact. For instance, changing a cylinder to a cone also changes the object’s centre of mass, contour and local contrast.

This approach is essentially a simpler, more experimentally transparent alternative to Quaddles.

My rating for IED use: 4/5.

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5. Superformula or Fourier “supershapes”

The Gielis superformula and related superellipse functions can generate organic, star-like, polygonal and flower-like contours from a compact set of parameters. Fourier-descriptor spaces provide even more general control. [5]

These could generate:

• rounded bodies;
• polygonal bodies;
• multi-lobed bodies;
• asymmetric amoebae;
• leaf-like bodies;
• star-shaped organisms.

They are most useful as the shape engine inside a microorganism generator, rather than as a complete multidimensional stimulus family.

One caveat is that radial-frequency patterns occupy a perceptually restricted subset of possible planar shapes, so I would combine low-frequency radial components with modest random Fourier perturbations rather than relying on a single frequency parameter. [2]

My rating as a shape generator: 5/5.

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6. Motion-augmented objects

Motion can function as an independent dimension:

• clockwise versus anticlockwise rotation;
• upward versus downward internal flow;
• expansion versus contraction;
• leftward versus rightward texture drift;
• regular versus irregular pulsation;
• appendages waving inward versus outward.

A touchscreen study in rhesus macaques and humans successfully used shape, colour and motion direction as three visual dimensions. Both species learned and shifted between motion-, colour- and shape-based rules, making motion a credible alternative to quantity for cross-species cognitive-flexibility testing. [6]

Why motion may be preferable to hair count

The attached stimuli use hair number and internal dot number. Both can become numerosity or density judgments rather than object-feature judgments. The comparative set-shifting literature has specifically noted that quantity may involve somewhat different computations and may be harder to match to shape and colour than motion. [6]

A stronger design would therefore keep hair number constant and manipulate:

• hair curvature;
• hair orientation;
• hair movement;
• hair length;
• terminal shape.

My rating as an optional third dimension: 4.5/5.

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7. Greebles and Ziggerins

Greebles and Ziggerins are established novel-object stimulus classes. Greebles have a common arrangement of parts and were designed particularly for studying expertise and face-like configural processing. Ziggerins have similarly been used for novel-object expertise training. [7]

They would not be my first choice for IED because:

• feature dimensions are not cleanly factorial;
• objects are strongly configural;
• part discriminability may be unequal;
• extensive exposure can change processing strategy;
• identity and dimension learning may become difficult to separate.

They are more useful for testing configural expertise than attentional set formation.

My rating for IED use: 2.5/5.

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8. AI-generated imaginary objects

The IMAGINE dataset contains 400 GAN-generated novel objects, with quantified size, contrast, luminance, colourfulness, edge density, entropy, symmetry and complexity. The objects are realistic-looking but unfamiliar. [8]

These would make useful:

• generalisation probes;
• novelty controls;
• engagement controls;
• object-memory stimuli.

However, they are not ideal for the main IED task because their generative variables do not correspond reliably to clean psychological dimensions. Two nearby points in an AI latent space may change texture, shape, colour and semantic appearance simultaneously.

My rating for the primary IED stimulus space: 2/5.

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2. Recommended architecture

I would construct a four-dimensional microorganism library, but use only two dimensions within any one CANTAB-style IED sequence.

For example:

Library dimension	Parameterisation
Shape	contour frequency, phase and curvature
Surface	spots, stripes, cellular, smooth
Appendages	straight, curved, forked, club-ended
Colour	calibrated hue at matched luminance

Then generate different task versions:

1. Shape versus texture
2. Shape versus appendage type
3. Colour versus texture
4. Colour versus appendage type
5. Shape versus motion
6. Texture versus motion

This allows you to examine whether ED costs generalise across different pairs of dimensions rather than depending on one privileged combination.

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3. A CANTAB-faithful nine-stage implementation

A microorganism version could preserve the original task logic:

Stage	Stimulus construction
1. SD	Two body shapes, no surface feature
2. SDR	Reward contingencies reversed
3. CD1	Surface patterns introduced adjacent to the bodies
4. CD2	Surface patterns moved inside the bodies
5. CDR	Reward contingencies reversed
6. IDS	New body shapes and new patterns; shape remains relevant
7. IDR	Reward contingencies reversed
8. EDS	New shapes and patterns; pattern becomes relevant
9. EDR	Reward contingencies reversed

The gradual progression from separate to compound dimensions mirrors the standard CANTAB arrangement, in which the second dimension is initially presented separately and then overlaid on the first. [9]

For a shape-appendage version:

• CD1 could show appendages as a separate halo or icon beside the body.
• CD2 could attach those appendages to the organism.
• The relevant rule could remain body shape until the ED shift.

This gives a rather elegant analogue of the original lines-and-shapes construction.

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4. Concrete microorganism generator

4.1 Shape layer

Generate the boundary from radial Fourier components:

base_radius
aspect_ratio
radial_frequency_1
radial_amplitude_1
radial_phase_1
radial_frequency_2
radial_amplitude_2
radial_phase_2
asymmetry
smoothing

Example shape families:

• smooth oval;
• triangular-lobed;
• five-lobed;
• seven-lobed;
• asymmetric amoeba;
• angular or crystalline.

After generation, normalise:

• enclosed area;
• maximum width and height;
• centroid;
• mean radius.

This prevents one shape from simply being larger or more eccentric.

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4.2 Appendage layer

Place appendages at equal arc-length intervals around the boundary rather than equal angular intervals. That avoids clustering them around elongated portions of the object.

Potential parameters:

appendage_count
appendage_length
appendage_width
appendage_curvature
appendage_orientation
appendage_tip
appendage_jitter

For a clean IED dimension, I recommend:

• fix count;
• fix total appendage ink;
• vary shape or curvature.

For example:

• straight versus curved;
• inward-pointing versus outward-pointing;
• pointed versus rounded tips;
• single versus bifurcated ends.

This avoids turning the task into sparse-versus-dense or few-versus-many classification.

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4.3 Texture layer

Generate textures inside a clipping mask defined by the body contour:

• Poisson-disc spots;
• sinusoidal stripes;
• concentric waves;
• Voronoi cell boundaries;
• checker patterns;
• band-limited noise;
• bubble-like inclusions.

Important texture parameters include:

texture_family
spatial_frequency
element_size
orientation
contrast
phase
coverage

Match:

• mean luminance;
• RMS contrast;
• total covered area;
• approximate edge density.

Thus “spots” cannot be selected merely because they are darker or contain more edges than “stripes”.

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4.4 Colour layer

Store colour in a device-independent or perceptually organised representation, while rendering through a calibrated monitor profile.

Parameters might include:

hue
chroma
luminance
gradient_strength
specular_strength

For the initial version:

• hold luminance approximately constant;
• use well-separated hues;
• avoid highly saturated red versus dim blue, which produces a luminance cue;
• verify all selected colours on the actual touchscreen.

For monkey testing, colour discriminability should ultimately be behaviourally calibrated on the target display rather than assumed from nominal RGB distances.

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5. A reproducible dataset specification

Every stimulus should be generated from a manifest rather than from filenames alone.

For example:

{
  "stimulus_id": "microbe_0042",
  "seed": 18371,
  "task_set": "shape_texture_A",
  "outline": {
    "frequency": 5,
    "amplitude": 0.16,
    "phase": 0.72,
    "aspect_ratio": 1.05,
    "asymmetry": 0.03
  },
  "appendages": {
    "type": "curved",
    "count": 16,
    "length": 0.11,
    "width": 0.012
  },
  "texture": {
    "type": "spots",
    "scale": 0.09,
    "contrast": 0.30,
    "coverage": 0.22
  },
  "colour": {
    "hue": 280,
    "luminance": 55,
    "chroma": 42
  }
}

The generator should output:

stimuli/
    svg/
    png/
    thumbnails/
    masks/
    metadata.csv
    metadata.json
    quality_control.csv

I would retain the SVG source even if Psychtoolbox ultimately presents PNG textures. SVG makes the objects inspectable and editable, while prerendered PNGs avoid unpredictable rasterisation during experimental trials.

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6. Dataset sampling strategy

Full latent space

Suppose the library contains:

• 12 shape exemplars;
• 8 appendage morphologies;
• 8 textures;
• 8 colours.

That nominally gives:

[ 12 \times 8 \times 8 \times 8 = 6144 ]

possible combinations before including continuous variation.

You should not necessarily render the whole factorial space. Instead:

1. Generate a large candidate pool.
2. Reject stimuli failing image-metric constraints.
3. Divide remaining objects into stage-specific sets.
4. Reserve completely held-out seeds for IDS and EDS.
5. Counterbalance which dimension becomes relevant first.

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Stage-specific exemplar allocation

Crucially, do not reuse the same shapes with merely a different texture during the IDS and EDS.

Reserve independent exemplars:

SD/SDR:     shape seeds 001-002
CD1/CD2:    same shape seeds + texture seeds 101-102
IDS/IDR:    new shape seeds 003-004 + texture seeds 103-104
EDS/EDR:    new shape seeds 005-006 + texture seeds 105-106

This ensures that successful transfer reflects attention to a dimension rather than memorisation of particular object identities.

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7. Perceptual calibration

The published Quaddle work emphasised the value of making features similarly discriminable and quantifying residual response biases. [10] That principle is even more important when constructing your own object space.

7.1 Single-dimension discrimination

Test each dimension in isolation:

• same/different;
• odd-one-out;
• two-alternative discrimination;
• matching-to-sample.

Estimate accuracy and latency as a function of parameter distance.

Select stimulus levels that produce approximately matched performance across dimensions.

For example:

shape A versus shape B:       88% correct
texture A versus texture B:   87% correct
colour A versus colour B:     89% correct
appendage A versus B:         86% correct

You do not want:

colour:    99%
shape:     83%
texture:   69%

because the ED result will then partly measure feature salience.

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7.2 Test dimensional separability

The dimensions should be evaluated in both:

• control blocks, where the irrelevant dimension is constant;
• filtering blocks, where the irrelevant dimension varies.

Slower or less accurate classification when the irrelevant dimension varies indicates Garner-type interference and suggests that the dimensions are not fully separable. Garner paradigms remain a standard way of assessing whether multidimensional stimuli can be selectively processed. [11]

Some interference is acceptable—and may even be theoretically interesting—but it should be measured rather than left unknown.

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7.3 Counterbalance dimensional preference

Across animals or participants, counterbalance:

• shape-first versus texture-first;
• colour-first versus appendage-first;
• which exemplar within a dimension is initially rewarded;
• left-right stimulus position;
• exact stage-specific stimulus set.

The classic human and nonhuman-primate work found better transfer when the previously relevant dimension remained relevant than when attention had to shift to the previously irrelevant dimension. [12] A systematic initial bias toward colour or shape could either enlarge or conceal that difference.

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8. Specific issues visible in the attached example

The screenshot is visually appealing, but several variables appear correlated:

1. The more irregular upper-right object also has more numerous appendages.
2. The smooth upper-left object has relatively few appendages.
3. The lower-right object differs in both aspect ratio and apparent appendage density.
4. The number of internal yellow dots varies.
5. Appendages are partly hidden against the dark rim.
6. The large circular and elliptical objects occupy somewhat different areas.
7. The upper objects have lighter gradients than the lower ones.

Those correlations are harmless in a children’s classification game, but problematic for an IED experiment. A subject could solve “shape” using:

• perimeter complexity;
• hair density;
• dot number;
• average luminance;
• object size.

I would therefore separate the rendering parameters aggressively:

• identical hair count across shape levels;
• identical spot count or texture coverage;
• equalised enclosed area;
• equalised mean luminance;
• controlled edge density;
• no drop shadow during the initial validation;
• appendages kept fully inside the selectable area and away from the screen boundary.

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9. Quaddles versus microorganisms

Quaddles are particularly strong when you need:

• genuine 3-D objects;
• viewpoint changes;
• rotating stimuli;
• object-part attention;
• later integration into Unity or augmented reality.

The original Quaddle set was designed so features remain visible around the vertical axis, can be adjusted for comparable discriminability, and can be exported as still images, rotating videos or FBX models. [10] Quaddle 2.0 adds a Blender-based generation workflow with several controllable body and part parameters and integration with Psychtoolbox and PsychoPy workflows. [13]

The microorganism approach is stronger when you need:

• a close CANTAB analogue;
• thousands of trial-unique exemplars;
• exact factorisation of dimensions;
• deterministic touchscreen rendering;
• SVG or MATLAB-native generation;
• minimal dependence on viewpoint and lighting.

My practical recommendation

Use two complementary stimulus systems:

Primary IED battery

2-D procedural microorganisms

• shape;
• texture;
• appendage morphology;
• colour;
• optional motion.

Generalisation battery

Quaddles or RUBubbles

• test whether the measured shift cost generalises from simple feature-factorised glyphs to richer 3-D objects.

That separation would let you distinguish a genuine attentional-set deficit from difficulty parsing one particular kind of complex object.

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References

1. Cambridge Cognition — Intra-Extra Dimensional Set Shift (IED)
2. ScienceDirect — Article on radial-frequency contour stimuli
3. RUBubbles: a configurable artificial-object stimulus set
4. Fribbles as multipart novel-object stimuli
5. Springer — Superformula-based parametric shape generation
6. Cross-species set shifting using shape, colour, and motion
7. Greebles and Ziggerins as novel-object expertise stimuli
8. IMAGINE: a dataset of GAN-generated unfamiliar objects
9. Description of the nine-stage intra-/extra-dimensional set-shifting procedure
10. Quaddles: a multidimensional parametric object set
11. Garner interference and dimensional separability
12. Classic comparative work on intra- and extradimensional shifts
13. Quaddle 2.0 generation workflow