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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

BP31 One line vs. two lines.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP26 BP27 BP28 BP29 BP30  *  BP32 BP33 BP34 BP35 BP36

KEYWORD

easy, precise, allsorted, left-narrow, right-narrow, pixelperfect, traditional, bongard

CONCEPT distinguishing_crossing_curves (info | search),
one (info | search),
two (info | search)

WORLD

smooth_crosscurves [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP210 Part of at least one object is out of box vs. all objects are within the box.
(edit; present; nest [left/right]; search; history)
COMMENTS

Alternatively, "black touches the boundary vs. not".

CROSSREFS

Adjacent-numbered pages:
BP205 BP206 BP207 BP208 BP209  *  BP211 BP212 BP213 BP214 BP215

KEYWORD

precise, boundingbox, perfect, pixelperfect, traditional, bordercontent

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

AUTHOR

Giuseppe Insana

BP211 More black than white vs. more white than black.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP196 for a version of this Problem restricted to uniform textures.

Adjacent-numbered pages:
BP206 BP207 BP208 BP209 BP210  *  BP212 BP213 BP214 BP215 BP216

KEYWORD

easy, nice, spectrum, dual, blackwhite, unstable, right-null, perfect, pixelperfect, traditional, continuous, viceversa, bordercontent

CONCEPT outlined_filled (info | search),
size (info | search),
texture (info | search)

WORLD

bmp [smaller | same | bigger]
zoom in left | zoom in right

AUTHOR

Giuseppe Insana

BP217 Totally black lines vs. lines with white specks.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP212 BP213 BP214 BP215 BP216  *  BP218 BP219 BP220 BP221 BP222

KEYWORD

perfect, pixelperfect

CONCEPT curve_texture (info | search),
texture (info | search)

AUTHOR

Giuseppe Insana

BP279 The left part has more pixels (area) than the right part vs. the left part has fewer pixels than the right part.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP274 BP275 BP276 BP277 BP278  *  BP280 BP281 BP282 BP283 BP284

KEYWORD

dual, handed, leftright, pixelperfect

CONCEPT left_right (info | search),
length_line_or_curve (info | search),
area (info | search)

WORLD

arial_font_two_symbols [smaller | same | bigger]

AUTHOR

Merse E. Gáspár

BP321 Small round object unreachable from the border of the box vs. small round object reachable from the border of the box.
(edit; present; nest [left/right]; search; history)
COMMENTS

Equivalently, "small round object enclosed by white loop vs. not so."

CROSSREFS

Adjacent-numbered pages:
BP316 BP317 BP318 BP319 BP320  *  BP322 BP323 BP324 BP325 BP326

KEYWORD

nice, precise, allsorted, boundingbox, perfect, pixelperfect, traditional, bordercontent

CONCEPT bounding_box (info | search),
path (info | search),
reachable (info | search)

AUTHOR

Aaron David Fairbanks

BP324 Left shapes can be placed on top of each other to make right shape vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP319 BP320 BP321 BP322 BP323  *  BP325 BP326 BP327 BP328 BP329

KEYWORD

precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional

CONCEPT set_union (info | search),
same_shape (info | search),
same (info | search)

AUTHOR

Aaron David Fairbanks

BP325 Left shapes can combine by symmetric difference (XOR logical operator) to make right shape vs. left shapes can combine by intersection (AND logical operator) to make right shape.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP320 BP321 BP322 BP323 BP324  *  BP326 BP327 BP328 BP329 BP330

KEYWORD

precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional

CONCEPT xor (info | search),
overlap (info | search)

AUTHOR

Aaron David Fairbanks

BP335 Tessellates the plane vs. does not tessellate the plane.
(edit; present; nest [left/right]; search; history)
COMMENTS

EX7152 is an example of a shape than can be stretched in such a way that it no longer tessellates the plane. This is a property that is only exhibited by shapes that tessellate with rotated copies of themselves. - Leo Crabbe, Mar 05 2021

CROSSREFS

Adjacent-numbered pages:
BP330 BP331 BP332 BP333 BP334  *  BP336 BP337 BP338 BP339 BP340

KEYWORD

nice, stretch, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, pixelperfect, traditional

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

WORLD

shape [smaller | same | bigger]
zoom in left (fill_shape)

AUTHOR

Aaron David Fairbanks

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