Left examples are sometimes called "rep-tiles."

The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.

Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."

See BP532 for a version with fractals.

Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343  *  BP345 BP346 BP347 BP348 BP349

Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.

hard, nice, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional

shape [smaller | same | bigger]

Aaron David Fairbanks

Left examples have the keyword "unstable" on the OEBP.

Right examples have the keyword "stable" on the OEBP.

For the purposes of this Bongard Problem, "small change" means adding to or removing from an arbitrarily small portion of the image. Other kinds of small change could be explored, such as making changes in multiple small places, translating, rotating, scaling, or deforming the whole image slightly (see also keywords deformunstable vs. deformstable), or even context-dependent small changes (e.g., changing the shadings slightly in BP196, or making small 3d changes to the represented 3d objects in BP333), but they are not considered here.

In a "stable" Bongard Problem, no small change should outright flip an example's sorting. It is allowed for a small change to make an example sorted slightly more ambiguously.

Small changes that make an example no longer even fit in with the format of a Bongard Problem are not considered. (Otherwise, far fewer Bongard Problems would be called "stable".)

For whether small changes make an example no longer fit in with the Bongard Problem, see unstableworld vs. stableworld.

If a Bongard Problem is shown with imperfect hand drawings (keyword ignoreimperfections), it is fine to apply the keyword "unstable" ignoring this. For instance, a hand-drawn version of BP344 would still be tagged "unstable", even though it would show examples wrong by small amounts.

(Note: a BP would only be tagged "ignoreimperfections" in the first place if the underlying idea were such that several small changes could make an example switch sides, no longer fit in with the format of the Bongard Problem, or otherwise be ambiguously sorted.)

Stable Bongard Problems are generally perfect and pixelperfect.

Gap (technically) implies stable. (However, in practice it has seemed unnatural to tag BPs "stable" when ALL small changes render certain examples unsortable, as is sometimes the case in "gap" BPs.)

Unstable Bongard Problems are often precise.

Stable Bongard Problems tend to either be fuzzy or otherwise either have a gap or be not allsorted.

See BP1144, which is about all small changes making all examples unsortable rather than some small change making some example switch sides.

See BP1140, which is about any (perhaps large) additions of detail instead of small changes.

Adjacent-numbered pages:
BP958 BP959 BP960 BP961 BP962  *  BP964 BP965 BP966 BP967 BP968

BP1 is unstable because it's possible to change nothing slightly by adding a pixel to end up with something.

meta (see left/right), links, keyword, stability

Aaron David Fairbanks

Left examples have the keyword "perfect" on the OEBP.

Right examples have the keyword "ignoreimperfections".

Consider the difference in style between BP344 and BP24.

Hand-drawn figures in BPs are typically imperfect. A "circles vs. squares" BP may only show what are approximately circles and approximately squares. A pedant might append to the solutions of all Bongard Problems the caveat "...when figures are interpreted as the most obvious shapes they approximate."

This is the meaning of the label "ignoreimperfections". On the other hand, the label "perfect" means even the pedant would drop this caveat; either all the images are precise, or precision doesn't matter (see also keyword stable).

Even in BPs tagged "perfect", the tiny rough edges caused by image pixelation are not expected to matter. If the OEBP would indeed prefer users only upload pixel-perfect examples, a BP can be tagged with the stricter keyword pixelperfect.

E.g., for BPs having to do with smooth curves and lines, "perfect" only requires images offer the best possible approximation of those intended shapes given the resolution.

Most Bongard Problems involving small details at all would be tagged "perfect". However, this is not always so; sometimes the small details are intended to be noticed, but certain imperfections are still intended to be overlooked.

BP119 ("small correction results in circle vs. not") is an interesting example: imperfections matter with respect to the outline being closed, but imperfections do not matter with respect to circular-ness.

If a Bongard Problem on the OEBP is tagged "ignoreimperfections" -- i.e., it has imperfect hand drawings -- then other keywords are generally applied relative to the intended idea, a corrected version sans imperfect hand drawings. (For example, this is how the keywords precise and stable are applied. Alternative versions of these keywords, which factor in imperfect hand drawings, could be made instead, but that would be less useful.)

It may be better to change the definition of "perfect" so it only applies to Bongard Problems such that small changes can potentially switch an example's side / remove it from the Bongard Problem. That would cut down on the number of Bongard Problems to label "perfect". There isn't currently a single keyword for "small changes can potentially switch an example's side / remove it from the Bongard Problem", but this is basically captured by unstable or unstableworld. There is also deformunstable which uses a different notion of "small change". - Aaron David Fairbanks, Jun 16 2023

See BP508 for discussion of this topic in relation to Bongard Problems tagged precise.

Stable Bongard Problems are generally "perfect".

Pixelperfect implies "perfect".

The keywords proofsrequired and noproofs (BP1125) have a similar relationship: "noproofs" indicates a lenience for a certain kind of imperfection.

Adjacent-numbered pages:
BP908 BP909 BP910 BP911 BP912  *  BP914 BP915 BP916 BP917 BP918

Many Bongard Problems involving properties of curves (e.g. BP62) really are about those wiggly, imperfect curves; they qualify as "perfect" problems. On the other hand, Bongard Problems involving polygons, (e.g. BP5) often show only approximately-straight lines; they are not "perfect" problems.

Bongard Problems with world "bmp" should be "perfect".

meta (see left/right), links, keyword, wellfounded

visualbp [smaller | same | bigger]
zoom in left (perfect_bp)

Aaron David Fairbanks

This is BP344 ("rep-tiles") but for fractals.

See BP1119 for the version with multiple different sizes of tile allowed.

Adjacent-numbered pages:
BP527 BP528 BP529 BP530 BP531  *  BP533 BP534 BP535 BP536 BP537

hardsort, proofsrequired, perfect, infinitedetail, contributepairs

[smaller | same | bigger]
zoom in left (fractal_self_tile)

Aaron David Fairbanks