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BP85 Three parts vs. five parts.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 242.

CROSSREFS

Adjacent-numbered pages:
BP80 BP81 BP82 BP83 BP84  *  BP86 BP87 BP88 BP89 BP90

KEYWORD

nice, number, finished, traditional, bongard

CONCEPT number (info | search),
three (info | search),
five (info | search)

AUTHOR

Mikhail M. Bongard

BP86 Three parts vs. five parts.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 242.

CROSSREFS

Adjacent-numbered pages:
BP81 BP82 BP83 BP84 BP85  *  BP87 BP88 BP89 BP90 BP91

KEYWORD

number, finished, traditional, bongard

CONCEPT branch_point (info | search),
lines_coincide (info | search),
number (info | search),
three (info | search),
five (info | search)

AUTHOR

Mikhail M. Bongard

BP87 Four parts vs. five parts.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 242.

CROSSREFS

Adjacent-numbered pages:
BP82 BP83 BP84 BP85 BP86  *  BP88 BP89 BP90 BP91 BP92

KEYWORD

number, finished, traditional, bongard

CONCEPT number (info | search),
four (info | search),
five (info | search)

AUTHOR

Mikhail M. Bongard

BP88 Three parts vs. five parts.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.

CROSSREFS

Adjacent-numbered pages:
BP83 BP84 BP85 BP86 BP87  *  BP89 BP90 BP91 BP92 BP93

KEYWORD

number, finished, traditional, bongard

CONCEPT number (info | search),
separation_of_joined_objects (info | search),
three (info | search),
five (info | search)

AUTHOR

Mikhail M. Bongard

BP89 Three parts vs. five parts.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 243.

CROSSREFS

Adjacent-numbered pages:
BP84 BP85 BP86 BP87 BP88  *  BP90 BP91 BP92 BP93 BP94

KEYWORD

number, finished, traditional, bongard

CONCEPT number (info | search),
feature_cluster (info | search),
cluster_of_one (info | search),
cluster (info | search),
three (info | search),
five (info | search)

AUTHOR

Mikhail M. Bongard

BP231 Five concavities vs. not five concavities.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP226 BP227 BP228 BP229 BP230  *  BP232 BP233 BP234 BP235 BP236

KEYWORD

less, noisy, arbitrary, traditional

CONCEPT indentation (info | search),
number (info | search),
five (info | search)

AUTHOR

Giuseppe Insana

BP302 5 collinear objects, of which the 3rd is moved elsewhere vs. 5 collinear objects, of which the 2nd/4th is moved elsewhere.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP297 BP298 BP299 BP300 BP301  *  BP303 BP304 BP305 BP306 BP307

KEYWORD

traditional

CONCEPT collinear (info | search),
ordinal_orering (info | search),
two (info | search),
three (info | search),
four (info | search),
five (info | search)

AUTHOR

"Lewis"

BP531 Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself.
(edit; present; nest [left/right]; search; history)
COMMENTS

More specifically, all left examples shown in this Problem have Hausdorff dimension log2(3) while all right examples have Hausdorff dimension log3(5).


Left examples can tile themselves by any power of 3 smaller same-sized copies of themselves while right examples can tile themselves by any power of 5 smaller same-sized copies of themselves.


Homage to Bongard's original three versus five Problems.

CROSSREFS

Adjacent-numbered pages:
BP526 BP527 BP528 BP529 BP530  *  BP532 BP533 BP534 BP535 BP536

KEYWORD

perfect, infinitedetail

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

WORLD

fractal_self_tile [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1048 Colors divide dots into some fifths vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1043 BP1044 BP1045 BP1046 BP1047  *  BP1049 BP1050 BP1051 BP1052 BP1053

KEYWORD

precise, allsorted, arbitrary, preciseworld

CONCEPT ratio (info | search),
five (info | search)

WORLD

outline_or_fill_circles_same_size [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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