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BP529 Fractal tiles itself with smaller non-rotated (nor reflected) copies of itself vs. fractal requires turning to tile itself.
(edit; present; nest [left/right]; search; history)
COMMENTS

No included examples involve reflection.

CROSSREFS

Adjacent-numbered pages:
BP524 BP525 BP526 BP527 BP528  *  BP530 BP531 BP532 BP533 BP534

KEYWORD

perfect, infinitedetail

CONCEPT fractal (info | search),
rotation_required (info | search),
self-reference (info | search),
tiling (info | search)

WORLD

fractal_self_tile [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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

BP1237 Connected fractal vs. disconnected fractal.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1232 BP1233 BP1234 BP1235 BP1236  *  BP1238 BP1239 BP1240 BP1241 BP1242

KEYWORD

notso, perfect, infinitedetail

CONCEPT connected_component (info | search),
fractal (info | search)

WORLD

fractal_self_tile [smaller | same | bigger]
zoom in left (connected_fractal_self_tile)

AUTHOR

Jago Collins

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