Fractal is tiled by three smaller copies of itself vs. fractal is tiled by five smaller copies of itself.

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.

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.

An homage to Bongard's many three versus five Problems.

Fractal is tiled by three smaller versions of itself vs. fractal is tiled by five smaller versions of itself.

Fractal is tiled by three smaller versions of itself (minimum) vs. fractal is tiled by five smaller versions of itself (minimum).

Fractal is tiled by three smaller versions of itself (minimum) vs. fractal is tiles by five smaller versions of itself (minimum).

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.

Aaron David Fairbanks

Bongard Problems with "world" one simple thin black curve allowed to self-intersect and/or be closed vs. other Bongard Problems.

Bongard Problems about (perhaps multiple) simple 2D connected shape outlines.

Aaron David Fairbanks

Assumed contained in bounding box.

Bongard Problems with "world" one simple curve allowed to self-intersect and/or be closed vs. other Bongard Problems.

Bongard Problems with "world" one simple curve allowed to self-intersect and/or be closed.

Bongard Problems with "world" one simple curve allowed to self-intersect or be closed.

Bongard Problems with "world" (perhaps multiple) simple 2D closed or non-closed curves with self-intersections allowed.

Bongard Problems with "world" (perhaps multiple) simple 2D shape outlines.

Bongard Problems with "world" (perhaps multiple) simple 2D connected outlines.

Bongard Problems with "world" (perhaps multiple) simple 2D connected shape outlines.

Bongard Problem with "world" (perhaps multiple) simple 2D connected shape outlines.