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BP67 The right branch begins at a higher point than the left branch vs. the right branch begins at a lower point than the left branch.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.

CROSSREFS

Adjacent-numbered pages:
BP62 BP63 BP64 BP65 BP66  *  BP68 BP69 BP70 BP71 BP72

KEYWORD

precise, spectrum, dual, handed, leftright, finished, traditional, continuous, viceversa, bongard

CONCEPT above_below (info | search),
branch_point (info | search),
left_right (info | search),
on_sides_of_curve (info | search),
tracing_line_or_curve (info | search)

WORLD

curve_tree_one_branch_per_side [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP1241 Any point contained in (arbitrarily) smaller version of self vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Note if any point is contained in some smaller version of the whole, then any point is contained in arbitrarily smaller versions of the whole.


It isn't possible to unambiguously communicate in a picture whether or not a few specific points are included in the fractal. The pictures are interpreted as what is intuitively simplest. To make matters less ambiguous, all the fractals here contain all points arbitrarily close to points in them. (They are topologically closed. See also BP1239.)


The left hand side of this is a stronger condition than the left hand side of BP1116.

CROSSREFS

Adjacent-numbered pages:
BP1236 BP1237 BP1238 BP1239 BP1240  *  BP1242 BP1243 BP1244 BP1245 BP1246

KEYWORD

notso, perfect, infinitedetail

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

connected_fractal [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1228 Frieze pattern with glide reflection symmetry vs. not.
(edit; present; nest [left/right]; search; history)
COMMENTS

Each example on the left is imagined to continue beyond the bounding box.

CROSSREFS

Adjacent-numbered pages:
BP1223 BP1224 BP1225 BP1226 BP1227  *  BP1229 BP1230 BP1231 BP1232 BP1233

KEYWORD

stub, notso, traditional, bordercontent, seemslike

CONCEPT symmetry (info | search)

AUTHOR

Aaron David Fairbanks

BP82 The convex hull of the crosses forms an equilateral triangle vs. the convex hull of the crosses does not form an equilateral triangle.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 241.

CROSSREFS

Adjacent-numbered pages:
BP77 BP78 BP79 BP80 BP81  *  BP83 BP84 BP85 BP86 BP87

KEYWORD

noisy, notso, finished, traditional, bongard

CONCEPT convex_hull (info | search),
equilateral_triangle (info | search),
triangle (info | search)

WORLD

[smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP1005 The collection of dot clumps has the same numerical property as each of the dot clumps vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

This is a version of BP999 with only numbers.

Contrast BP1006, which is very similar.

Adjacent-numbered pages:
BP1000 BP1001 BP1002 BP1003 BP1004  *  BP1006 BP1007 BP1008 BP1009 BP1010

KEYWORD

nice, notso, hardsort, left-narrow, rules

CONCEPT recursion (info | search),
self-reference (info | search)

WORLD

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

AUTHOR

Aaron David Fairbanks

BP312 Lines intersect within the box vs. lines intersect out of the box.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP307 BP308 BP309 BP310 BP311  *  BP313 BP314 BP315 BP316 BP317

KEYWORD

precise, allsorted, boundingbox, perfect, unorderedpair, traditional, preciseworld, absoluteposition

CONCEPT completed_out_of_box (info | search),
vertex_of_meeting_lines (info | search),
imagined_point (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Jakub Štepo

BP133 Dots collinear with center of circle vs. dots not collinear with center of circle.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP128 BP129 BP130 BP131 BP132  *  BP134 BP135 BP136 BP137 BP138

KEYWORD

traditional

CONCEPT all (info | search),
collinear (info | search),
center_of_circle (info | search),
center (info | search),
imagined_point (info | search),
imagined_entity (info | search)

AUTHOR

Douglas R. Hofstadter

BP1012 No tile shares a partial side with another tile vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1007 BP1008 BP1009 BP1010 BP1011  *  BP1013 BP1014 BP1015 BP1016 BP1017

KEYWORD

precise, allsorted, perfect

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

WORLD

wallpaper_tiling_1_polygon [smaller | same | bigger]
zoom in left

AUTHOR

Leo Crabbe

BP937 Shapes have equal perimeter vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP932 BP933 BP934 BP935 BP936  *  BP938 BP939 BP940 BP941 BP942

KEYWORD

precise, allsorted, unstable, left-narrow, perfect, unorderedpair

CONCEPT perimeter (info | search)

WORLD

2_fill_shapes [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1057 Filled subsection divides the grid vs. not so
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1052 BP1053 BP1054 BP1055 BP1056  *  BP1058 BP1059 BP1060 BP1061 BP1062

KEYWORD

math, grid, left-listable, right-listable

CONCEPT division (info | search),
tiling (info | search)

WORLD

zoom in left

AUTHOR

Jago Collins

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