The On-Line Encyclopedia of Bongard Problems

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BP1002

Vaguely self-similar (looks like self-similar fractal after one iteration) vs. not so.

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	CROSSREFS	`See BP1004 for a Problem about conceptual self-similarity instead of visual self-similarity.` `See BP188 for a similar Problem restricted to shape outlines made of shape outlines.` `Adjacent-numbered pages: BP997 BP998 BP999 BP1000 BP1001 * BP1003 BP1004 BP1005 BP1006 BP1007`
	KEYWORD	`easy, nice, fuzzy, abstract, anticomputer, concept, traditional`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `similar_shape (info \| search),` `similar (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1003

The combined collection obeys the same rule as the sub-collections vs. not so.

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	COMMENTS	`Since it is most intuitive to imagine spatially squishing together all the collections in the process of combining them into one big collection, avoid rules that involve relative spatial positionings of objects.`
	CROSSREFS	`Contrast BP999, which is very similar. There, when considering the whole picture, the collections are to be treated as individual objects; here, when considering the whole picture, the collections are to be combined into one big collection. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.` `Also contrast BP1004, which is about a collection of plain objects obeying the same rule as all the objects (instead of a collection of [collections of objects] obeying the same rule as all the [collections of objects]).` `See BP1006 for the version with only number-based properties. All panels in that Bongard Problem fit the same way in this Bongard Problem as well.` `Adjacent-numbered pages: BP998 BP999 BP1000 BP1001 BP1002 * BP1004 BP1005 BP1006 BP1007 BP1008`
	KEYWORD	`nice, abstract, notso, creativeexamples, rules, miniworlds`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe, Aaron David Fairbanks`

BP1004

The whole satisfies the same rule as its parts vs. not so.

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	COMMENTS	`The "whole" is the entire panel including the bounding box. A "part" is some region either stylistically different or amply separated in space from everything else. Smaller parts-within-parts don't count as parts.` `Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)` `See BP793 and BP999 for similar paradoxes.`
	CROSSREFS	`See BP1006 for the version about numerical properties where each part is a cluster of dots; examples in that BP would be sorted the same way here that they are there.` `See BP999 and BP1003 for versions where each object is itself a collection of objects, so that the focus is on rules specifically pertaining to collections (e.g. "all the objects are different").` `See BP1002 for a Bongard Problem about only visual self-similarity instead of conceptual self-similarity.` `The rule shown in each panel is "narrow" (see BP513^left and BP514^left).` `Adjacent-numbered pages: BP999 BP1000 BP1001 BP1002 BP1003 * BP1005 BP1006 BP1007 BP1008 BP1009`
	KEYWORD	`nice, abstract, anticomputer, creativeexamples, left-narrow, rules, miniworlds`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1110

The process that turns one object into the other is the same both ways vs. the process changes depending on which object is chosen as the starting point.

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	REFERENCE	`https://en.wikipedia.org/wiki/Duality_(mathematics)` `https://en.wikipedia.org/wiki/Involution_(mathematics)`
	CROSSREFS	`This is a special case of BP841 and a generalisation of BP822.` `Adjacent-numbered pages: BP1105 BP1106 BP1107 BP1108 BP1109 * BP1111 BP1112 BP1113 BP1114 BP1115`
	KEYWORD	`nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1127

There is no rule for how the objects in a cluster interrelate vs. there is.

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	COMMENTS	`Other ways of phrasing this:` `"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.` `The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.`
	CROSSREFS	`Adjacent-numbered pages: BP1122 BP1123 BP1124 BP1125 BP1126 * BP1128 BP1129 BP1130 BP1131 BP1132`
	KEYWORD	`abstract, creativeexamples, left-unknowable, rules, miniworlds`
	CONCEPT	`local_global (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1155

Shapes are sorted according to a simple rule that uniquely determines where everything goes vs. shapes are sorted according to some other rule (or lack thereof).

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	CROSSREFS	`Adjacent-numbered pages: BP1150 BP1151 BP1152 BP1153 BP1154 * BP1156 BP1157 BP1158 BP1159 BP1160`
	KEYWORD	`abstract, unwordable, creativeexamples, right-unknowable, traditional, finishedexamples, rules`
	AUTHOR	`Leo Crabbe`

BP1157

The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.

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	COMMENTS	`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.`
	REFERENCE	`https://en.wikipedia.org/wiki/Commutative_property`
	CROSSREFS	`Adjacent-numbered pages: BP1152 BP1153 BP1154 BP1155 BP1156 * BP1158 BP1159 BP1160 BP1161 BP1162`
	KEYWORD	`nice, abstract, unwordable, notso, structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1191

One natural way of matching up the two collections vs. multiple natural ways of matching up the two collections.

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	COMMENTS	`Jago originally designed this as a triptych. EX9655, EX9656, and EX9657 belong in a third category displayed further right of the two categories shown here. The third category is "all possible ways of matching are equally natural". - Aaron David Fairbanks, Apr 18 2022`
	CROSSREFS	`Adjacent-numbered pages: BP1186 BP1187 BP1188 BP1189 BP1190 * BP1192 BP1193 BP1194 BP1195 BP1196`
	KEYWORD	`nice, abstract, creativeexamples, structure, miniworlds, dithering`
	AUTHOR	`Jago Collins`

BP1260

Same transformation applied to circle, triangle, and square vs. different transformations applied.

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	CROSSREFS	`BP839 is about applying opposite transformations to a single object.` `Adjacent-numbered pages: BP1255 BP1256 BP1257 BP1258 BP1259 * BP1261 BP1262 BP1263 BP1264 BP1265`
	KEYWORD	`easy, nice, abstract, arbitrary, anticomputer, left-null, structure, orderedtriplet, traditional, rules`
	CONCEPT	`circle (info \| search),` `analogy (info \| search),` `square (info \| search),` `same (info \| search),` `triangle (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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