This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.

Adjacent-numbered pages:
BP536 BP537 BP538 BP539 BP540  *  BP542 BP543 BP544 BP545 BP546

notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bp)

Aaron David Fairbanks

Adjacent-numbered pages:
BP537 BP538 BP539 BP540 BP541  *  BP543 BP544 BP545 BP546 BP547

notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bppage)

Aaron David Fairbanks

All ideas and things, with no limits.

Adjacent-numbered pages:
BP539 BP540 BP541 BP542 BP543  *  BP545 BP546 BP547 BP548 BP549

notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny

everything [smaller | same]
zoom in left (everything) | zoom in right (nothing)

Aaron David Fairbanks

Left-sorted BPs have the keyword "notso" on the OEBP.

This meta Bongard Problem is about Bongard Problems featuring two rules that are conceptual opposites.

Sometimes both sides could be seen as the "not" side: consider, for example, two definitions of the same Bongard Problem, "shape has hole vs. does not" and "shape is not filled vs. is". It is possible (albeit perhaps unnatural) to phrase the solution either way when the left and right sides partition all possible relevant examples cleanly into two groups (see the allsorted keyword).

When one property is "positive-seeming" and its opposite is "negative-seeming", it usually means the positive property would be recognized without counter-examples (e.g. a collection of triangles will be seen as such), while the negative property wouldn't be recognized without counter-examples (e.g. a collection of "non-triangle shapes" will just be interpreted as "shapes" unless triangles are shown opposite them).

BP513 (keyword left-narrow) is about Bongard Problems whose left side can be recognized without the right side. When a Bongard Problem is left-narrow and not "right-narrow that usually makes the property on the left seem positive and the property on the right seem negative.

The OEBP by convention has preferred the "positive-seeming" property (when there is one) to be on the left side.

All in all, the keyword "notso" should mean:

1) If the Bongard Problem is "narrow" on at least one side, then it is left-narrow.

2) The right side is the conceptual negation of the left side.

If a Bongard Problem's solution is "[Property A] vs. not so", the "not so" side is everything without [Property A] within some suitable context. A Bongard Problem "triangles vs. not so" might only include simple shapes as non-triangles; it need not include images of boats as non-triangles. It is not necessary for all the kitchen sink to be thrown on the "not so" side (although it is here).

See BP1001 for a version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP. (This version is a little different. In BP1001, the kitchen sink of all other possible images is always included on the right "not so" side, rather than a context-dependent conceptual negation.)

Contrast keyword viceversa.

"[Property A] vs. not so" Bongard Problems are often allsorted, meaning they sort all relevant examples--but not always, because sometimes there exist ambiguous border cases, unclear whether they fit [Property A] or not.

Adjacent-numbered pages:
BP862 BP863 BP864 BP865 BP866  *  BP868 BP869 BP870 BP871 BP872

notso, meta (see left/right), links, keyword, left-self, funny

everything [smaller | same]
zoom in left

Aaron David Fairbanks

Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.

See BP953, BP959.

Adjacent-numbered pages:
BP897 BP898 BP899 BP900 BP901  *  BP903 BP904 BP905 BP906 BP907

notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny

everything [smaller | same]
zoom in left (bp902)

Leo Crabbe

There are various problematic cases left out. Are black and white to be inverted within a fractal's convex hull or its outermost outline?

Must this outline be preserved around the smaller inverted version of the fractal, or is it allowed to bleed into other white areas?

No examples have been included in this Bongard Problem whose placement depends on these questions.

Adjacent-numbered pages:
BP1102 BP1103 BP1104 BP1105 BP1106  *  BP1108 BP1109 BP1110 BP1111 BP1112

perfect, infinitedetail

fractal [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1103 BP1104 BP1105 BP1106 BP1107  *  BP1109 BP1110 BP1111 BP1112 BP1113

right-null, perfect, infinitedetail, assumesfamiliarity, neither

fractal [smaller | same | bigger]

Aaron David Fairbanks

Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".

The left hand side of this is a weaker condition than the left hand side of BP1241.

Adjacent-numbered pages:
BP1111 BP1112 BP1113 BP1114 BP1115  *  BP1117 BP1118 BP1119 BP1120 BP1121

notso, perfect, infinitedetail

connected_fractal [smaller | same | bigger]

Aaron David Fairbanks

With mathematical jargon:

No distinct same-sized copies of self overlap on a subset with positive measure in the Hausdorff measure using the Hausdorff dimension.

For a covering of a fractal by finitely many scaled down copies of itself, the condition of that no two have an intersection with positive measure is equivalent to the condition that the Hausdorff dimension coincides with the similarity dimension.

(There is another similar condition in this context called the "open set condition" which implies this but is not equivalent. The open set condition is equivalent to the condition that the Hausdorff measure using the similarity dimension is nonzero.)

https://en.wikipedia.org/wiki/Hausdorff_dimension

https://en.wikipedia.org/wiki/Open_set_condition

Adjacent-numbered pages:
BP1115 BP1116 BP1117 BP1118 BP1119  *  BP1121 BP1122 BP1123 BP1124 BP1125

challenge, perfect, infinitedetail

[smaller | same | bigger]

Aaron David Fairbanks

Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.

It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)

The left hand side of this is a stronger condition than the left hand side of BP1116.

Adjacent-numbered pages:
BP1236 BP1237 BP1238 BP1239 BP1240  *  BP1242 BP1243 BP1244 BP1245 BP1246

notso, perfect, infinitedetail

connected_fractal [smaller | same | bigger]

Aaron David Fairbanks