code/distributed_scanning/attribute_group_counting/creation.md

Attribute Group Counting

Goal

Scatter many small visual elements across the canvas. All elements are the same color — groups are distinguished only by shape. Each shape is an irregular random blob generated via Fourier harmonics in polar coordinates. They cannot be described by simple geometric names (circle, square, etc.), forcing the model to perform visual pairing rather than textual identification. The model must scan the entire image, visually compare every element's silhouette, and count how many distinct groups have at least 2 members.

Element library

• Shapes: procedurally generated irregular blobs (random Fourier harmonics, 8-14 lobes, unique per group)
• Color: uniform dark gray for all elements (no color differentiation)
• Texture: solid fill for all elements (no texture differentiation)

A group identity is determined solely by shape. Each group has 2-5 elements, all sharing the exact same silhouette. There are no decoys (every element belongs to a group of size ≥2).

Question

"How many distinct groups of matching shapes are in the image? All shapes are the same color. Two shapes belong to the same group if and only if they have exactly the same silhouette. The shapes are irregular and cannot be described by simple geometric names — you must visually compare them. Count the number of distinct shape groups and report the total."

Generation

1. Pick K (number of groups), e.g. 4-9.
2. Generate K distinct random blob shapes using Fourier harmonics in polar coordinates.
3. For each group, sample size in 2-5.
4. Place all elements at random positions with minimum spacing so they don't overlap.
5. Render using matplotlib for smooth, anti-aliased outlines.
6. Store annotations.

GT = K.