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BP845 "Noisy" properties changing independent of the consistently increasing quantity vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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

CROSSREFS

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

KEYWORD

creativeexamples, structure, contributepairs, rules

WORLD

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

AUTHOR

Aaron David Fairbanks

BP846 A quantity increases by fixed constant amount each step vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

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

KEYWORD

creativeexamples, structure, contributepairs, rules

WORLD

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

AUTHOR

Aaron David Fairbanks

BP848 Lower bound object shown vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

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

KEYWORD

creativeexamples, structure, contributepairs, rules

WORLD

constant_change_seq_increase_right_low_bound_obj [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP850 Shape can be maneuvered around the corner vs. not so.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP845 BP846 BP847 BP848 BP849  *  BP851 BP852 BP853 BP854 BP855

KEYWORD

nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering

CONCEPT rotation_required (info | search),
imagined_motion (info | search),
physically_fitting (info | search)

AUTHOR

Leo Crabbe

BP852 Object shown below is the "limit" of the sequence above (end result after "infinite time") versus not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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).

CROSSREFS

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

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP855 Object below ambiguously sorted (not clearly left or right) by Bongard Problem image above vs. object below clearly sorted by Bongard Problem image above.
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

nice, creativeexamples, structure, rules

WORLD

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

AUTHOR

Aaron David Fairbanks

BP860 Finitely many copies of the shape can be arranged such that they are locked together vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

This is a generalisation of BP861.

Adjacent-numbered pages:
BP855 BP856 BP857 BP858 BP859  *  BP861 BP862 BP863 BP864 BP865

KEYWORD

hard, nice, stub, precise, stretch, unstable, hardsort, challenge, creativeexamples, perfect, pixelperfect

CONCEPT tiling (info | search)

WORLD

fill_shape [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP863 Two shapes can tessellate the plane together vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP858 BP859 BP860 BP861 BP862  *  BP864 BP865 BP866 BP867 BP868

KEYWORD

nice, precise, allsorted, math, hardsort, creativeexamples, unorderedpair

CONCEPT infinite_plane (info | search),
tessellation (info | search),
tiling (info | search)

WORLD

2_shapes [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP870 Increasing quantity has upper bound (will get "stopped" by something) vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Related to BP380.

CROSSREFS

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

KEYWORD

creativeexamples, structure, rules

WORLD

constant_change_seq_increase_right [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP893 As one quantity increases an equally obvious opposite quantity decreases vs. there is only one obvious quantity, which increases as the sequence progresses right.
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

creativeexamples, structure, rules

WORLD

constant_change_seq_increase_right [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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