Left examples are sometimes called "rep-tiles."

The tiles all must be the same size. More specifically, all left examples can tile themselves only using scaled down and rotated versions of themselves with all tiles the same size. Right examples cannot tile themselves using scaled down rotated versions of themselves or even reflected versions of themselves with all tiles the same size.

Without the puzzle piece-like shape EX4120 on the right side the current examples also allow the solution "shape can tile with itself so as to create a parallelogram vs. shape cannot tile with itself so as to create a parallelogram."

See BP532 for a version with fractals.

Adjacent-numbered pages:
BP339 BP340 BP341 BP342 BP343  *  BP345 BP346 BP347 BP348 BP349

Go to https://oebp.org/files/yet.png for an illustration of how some left-sorted shapes tile themselves.

hard, nice, precise, notso, unstable, math, hardsort, creativeexamples, proofsrequired, perfect, traditional

shape [smaller | same | bigger]

Aaron David Fairbanks

All examples in this Problem are solid black shapes.

This problem is absurdly hard. It makes a good extreme example. - Aaron David Fairbanks, Nov 23 2020

Adjacent-numbered pages:
BP554 BP555 BP556 BP557 BP558  *  BP560 BP561 BP562 BP563 BP564

hard, nice, precise, allsorted, notso, stretch, challenge, left-narrow, perfect

fill_shape [smaller | same | bigger]

Leo Crabbe

If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?

All examples in this Problem are connected line segments or curves.

We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point.

Adjacent-numbered pages:
BP559 BP560 BP561 BP562 BP563  *  BP565 BP566 BP567 BP568 BP569

Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left.

hard, nice, allsorted, solved, perfect

Leo Crabbe

Adjacent-numbered pages:
BP907 BP908 BP909 BP910 BP911  *  BP913 BP914 BP915 BP916 BP917

perfect, contributepairs

zoom in right (shape_outline)

Leo Crabbe

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

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

2_fill_shapes [smaller | same | bigger]

Leo Crabbe

Adjacent-numbered pages:
BP944 BP945 BP946 BP947 BP948  *  BP950 BP951 BP952 BP953 BP954

nice, precise, allsorted, stretch, perfect, traditional, preciseworld

3_or_4_points [smaller | same | bigger]

Leo Crabbe

Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.

Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.

See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.

Adjacent-numbered pages:
BP960 BP961 BP962 BP963 BP964  *  BP966 BP967 BP968 BP969 BP970

hard, precise, distractingworld, perfect

Aaron David Fairbanks