"Noisy" sequences of change vs. "minimalist" sequences of change.

See BP511 for noise in BPs.

See BP827 for noise in images of BPs.

Adjacent-numbered pages:
BP840 BP841 BP842 BP843 BP844  *  BP846 BP847 BP848 BP849 BP850

creativeexamples, structure, contributepairs, rules

quantity_change_seq_increase_right_noise_allowed [smaller | same | bigger]
zoom in right (quantity_change_seq_increase_right)

Aaron David Fairbanks

Adjacent-numbered pages:
BP841 BP842 BP843 BP844 BP845  *  BP847 BP848 BP849 BP850 BP851

creativeexamples, structure, contributepairs, rules

quantity_change_seq_increase_right [smaller | same | bigger]
zoom in right (constant_change_seq_increase_right)

Aaron David Fairbanks

Adjacent-numbered pages:
BP843 BP844 BP845 BP846 BP847  *  BP849 BP850 BP851 BP852 BP853

creativeexamples, structure, contributepairs, rules

constant_change_seq_increase_right_low_bound_obj [smaller | same | bigger]

Aaron David Fairbanks

The conceptual limit of the sequence may not be the limit of the points in the image. For example in a sequence of halvings the limit value is never reached, so the bottom would never change color and thus its limit would not would not either.

Sequences progress from left to right (and there is not usually a way to intuitively extend the sequence in the other direction).

Adjacent-numbered pages:
BP847 BP848 BP849 BP850 BP851  *  BP853 BP854 BP855 BP856 BP857

notso, creativeexamples, perfect, infinitedetail, assumesfamiliarity, structure, contributepairs, rules

Aaron David Fairbanks

Represented are Bongard Problems and an extra object to sort, a.k.a. the Bongard's Dozen format.

A variety of kinds of ambiguities showcased as left examples.

Adjacent-numbered pages:
BP850 BP851 BP852 BP853 BP854  *  BP856 BP857 BP858 BP859 BP860

nice, creativeexamples, structure, rules

bdimage_shapes_extra_below [smaller | same | bigger]
zoom in right (bdimage_shapes_extra_below_clear_sort)

Aaron David Fairbanks

Related to BP380.

Adjacent-numbered pages:
BP865 BP866 BP867 BP868 BP869  *  BP871 BP872 BP873 BP874 BP875

creativeexamples, structure, rules

constant_change_seq_increase_right [smaller | same | bigger]

Aaron David Fairbanks

Another way of phrasing the solution: "Neither direction would more naturally be called increase in quantity vs. rightward progression would be called an increase."

Most right examples shown are unboundedly increasing, since finite sequences showing a quantity increasing usually also suggest "distance to end of sequence" as a decreasing opposite quantity. Even so, there are some finite sequences with one direction more intuitively increase-like than the other.

Adjacent-numbered pages:
BP888 BP889 BP890 BP891 BP892  *  BP894 BP895 BP896 BP897 BP898

creativeexamples, structure, rules

constant_change_seq_increase_right [smaller | same | bigger]

Aaron David Fairbanks

All examples depict a process that transforms one object into another (two example input-output pairs are provided in every panel). In left-sorted examples, each input corresponds to a unique output, whereas in right-sorted examples, different inputs could potentially lead to the same output. There is a sense in which all the processes described on the right "lose" some amount of the input's information.

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

Adjacent-numbered pages:
BP912 BP913 BP914 BP915 BP916  *  BP918 BP919 BP920 BP921 BP922

nice, abstract, creativeexamples, structure, rules, miniworlds

Leo Crabbe

There are many ambiguities here. The solver is expected to determine what things are "allowed" to be inputs for each process. To avoid confusion examples should not be sorted differently if you consider inputting nothing.

In each example there is at least some overlap between the set of possible inputs and the set of possible outputs for each process. If we did not apply this constraint, an easy example to be sorted right would be a process that turns blue shapes red.

A harder-to-read but more clearly defined version of this Problem could include within each example a mini Bongard Problem sorting left all allowed inputs for the process.

https://en.wikipedia.org/wiki/Fixed_point_(mathematics)

Adjacent-numbered pages:
BP946 BP947 BP948 BP949 BP950  *  BP952 BP953 BP954 BP955 BP956

structure, rules, miniworlds

Leo Crabbe

All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.

Intentionally left out of this Problem (shown above sorted ambiguously) are cases in which the rule is not possible to deduce without seeing more squares. Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."

https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

BP1258 is very similar: whether ALL squares can be deduced from the rest.

Adjacent-numbered pages:
BP974 BP975 BP976 BP977 BP978  *  BP980 BP981 BP982 BP983 BP984

nice, notso, structure, rules, miniworlds

grid_of_images_with_rule_one_on_edge_missing [smaller | same | bigger]

Aaron David Fairbanks