This was created as an example of a distractingworld Bongard Problem. Each example shows a distractingly detailed scene, irrelevant to the solution.
Despite this distraction, the keyword noisy does not fit this Bongard Problem because only details relevant to the solution change between examples.
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easy, nice, arbitrary, example, distractingworld, experimental
Aaron David Fairbanks
Operations depicted in right-sorted examples are called "commutative".
"Order matters" here means that if the objects in the top half were to switch places, the output would look different.
https://en.wikipedia.org/wiki/Commutative_property
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nice, abstract, unwordable, notso, structure, rules, miniworlds
Leo Crabbe
Intuitively, if one imagines shaking the circles in each example, the polygons in right-sorted examples could be imagined to "rattle around".
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precise, allsorted, dithering