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BP1 Empty image vs. non-empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

The first Bongard Problem.

All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

CROSSREFS

Adjacent-numbered pages:
  *  BP2 BP3 BP4 BP5 BP6

EXAMPLE

A circle fits on the right because it is not nothing.

KEYWORD

easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard

CONCEPT empty (info | search),
existence (info | search),
zero (info | search)

WORLD

zoom in left (blank_image) | zoom in right (curves_drawing)

AUTHOR

Mikhail M. Bongard

BP21 Small shape present vs. all shapes large.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples in this problem include three or fewer outlines of circles and (non-skinny) triangles.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.

CROSSREFS

Adjacent-numbered pages:
BP16 BP17 BP18 BP19 BP20  *  BP22 BP23 BP24 BP25 BP26

KEYWORD

finished, traditional, bongard

CONCEPT existence (info | search),
size (info | search)

WORLD

circle_triangle_outlines [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP24 A circle vs. no circle.
(edit; present; nest [left/right]; search; history)
COMMENTS

All small squares appearing in this problem are axis-aligned.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.

CROSSREFS

Adjacent-numbered pages:
BP19 BP20 BP21 BP22 BP23  *  BP25 BP26 BP27 BP28 BP29

KEYWORD

finished, traditional, bongard

CONCEPT circle (info | search),
existence (info | search)

WORLD

circle_square_eq-tri_small_outlines [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP26 Solid black triangle vs. no solid black triangle.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.

CROSSREFS

Adjacent-numbered pages:
BP21 BP22 BP23 BP24 BP25  *  BP27 BP28 BP29 BP30 BP31

KEYWORD

finished, traditional, bongard

CONCEPT and (info | search),
existence (info | search),
outlined_filled (info | search),
feature_cluster (info | search),
cluster (info | search),
texture (info | search),
triangle (info | search)

WORLD

circle_eq-tri_small_some_outline_some_fill [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP30 A curve with one self-crossing vs. a curve without a self-crossing.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

CROSSREFS

BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.

Adjacent-numbered pages:
BP25 BP26 BP27 BP28 BP29  *  BP31 BP32 BP33 BP34 BP35

KEYWORD

nice, finished, traditional, bongard

CONCEPT x-crossing (info | search),
existence (info | search)

WORLD

crosscurve [smaller | same | bigger]
zoom in right (curve_or_outline)

AUTHOR

Mikhail M. Bongard

BP33 Acute angle vs. no acute angle.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.

CROSSREFS

Adjacent-numbered pages:
BP28 BP29 BP30 BP31 BP32  *  BP34 BP35 BP36 BP37 BP38

KEYWORD

nice, stretch, finished, traditional, bongard

CONCEPT acute (info | search),
angle (info | search),
existence (info | search)

WORLD

Multiple options:
mediumsize_centered_outline [smaller | same | bigger],
shape_outline [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP92 The chain does not branch vs. the chain branches.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.

CROSSREFS

Adjacent-numbered pages:
BP87 BP88 BP89 BP90 BP91  *  BP93 BP94 BP95 BP96 BP97

KEYWORD

finished, traditional, bongard

CONCEPT all (info | search),
branch_point (info | search),
collinear (info | search),
existence (info | search)

AUTHOR

Mikhail M. Bongard

BP118 No cycle vs. a cycle exists.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP113 BP114 BP115 BP116 BP117  *  BP119 BP120 BP121 BP122 BP123

KEYWORD

traditional

CONCEPT arrow (info | search),
cyclic_path (info | search),
existence (info | search),
path (info | search)

AUTHOR

Douglas R. Hofstadter

BP119 A small correction will result in a single circle vs. no small correction will result in a single circle.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP114 BP115 BP116 BP117 BP118  *  BP120 BP121 BP122 BP123 BP124

KEYWORD

fuzzy, traditional

CONCEPT existence (info | search),
imperfection_small (info | search)

WORLD

curves_drawing [smaller | same | bigger]

AUTHOR

Douglas R. Hofstadter

BP131 Dots are vertices of a parallelogram vs. dots are not vertices of a parallelogram.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP126 BP127 BP128 BP129 BP130  *  BP132 BP133 BP134 BP135 BP136

KEYWORD

noisy, traditional

CONCEPT existence (info | search),
length_line_or_curve (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Douglas R. Hofstadter

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