Oak cubes and hexagonal tilings

Mark Dow

Oak cubes and hexagonal tilings

All images are rendered from a single cropped chunk of DigiMorph CT data of Quercus robur (English or Peduncate Oak): Dr. Peter Gasson, 2002, "Quercus robur" (On-line), Digital Morphology. Accessed October 23, 2006 at http://digimorph.org/specimens/Quercus_robur/. The individal renderings were made using Space Software. Volume data for the cube: Oak_cube.vol.gz (8 MB).

Ambiguous Triple Cubes

48 Meta-Cube

16 Rotation Ambiguous Cubes

Fractal hexagonal tilings of cubes

Ambiguous Triple Cubes

3 segment rocking animation. (Best if viewed as a continuous loop/repeat.)
Ambiguous_Triple_Cube_small.avi 3.4 MB, 423 x 456 px.
Ambiguous_Triple_Cube.avi 12 MB, high resolution version: 846 x 912 px.

8 segment rotation animation, cropped. (Best if viewed as a continuous loop/repeat.)
Ambiguous_Triple_Cube_x2rHc320.wmv 2 MB, 320 x 240 px., 32 s
Ambiguous_Triple_Cube_x2rHc640.wmv 8 MB, high resolution version: 640 x 480 px., 32 s

Ambiguous_Triple_Cube.jpg (still image)

Motion resolves the depth ambiguities, but there are depth discontinuities at motion transitions. The discontinuities aren't apparent until sometime after the transitions, so the percept is smooth. This visual illusion is derived from Oscar Reutersvärd's "Impossible Triangle", which was popularized in the 1950's by Roger Penrose, and is sometimes called a "Penrose Triangle".
My percept of the "rocking" version is different than the "rotating" version: in the rotating version I often percieve the cubes to apparently slide to their new configuration.

48 Meta-Cube

48_Meta-Cube_o4.jpg (small)
48_Meta-Cube.jpg (large, 4 MB, 4900x4900 px.)
This figure is composed of all rotations (3x8 corners), including mirroring (x2), of the same cube.

16 Rotation Ambiguous Cubes

16_Rotation_Ambiguous_Cubes_xp4.jpg  (medium)
16_Rotation_Ambiguous_Cubes_o10.jpg  (small)
16_Rotation_Ambiguous_Cubes.jpg  (large)

A couple people have asked to use this image, and I am fond of it too. Kristel Braunius, a Graphic Designer in Holland, asked to use it in "a little book about 'clean language / communication' for the university of Wageningen in Holland." She sent the page proof (below), which is a nice juxtaposition of the image with a diagram of the human visual system. I wonder what the Dutch chapter title "Over de taal" means:

Fractal hexagonal tilings of cubes

$1 Cube, fractal hexagonal tiling$
1_Cube_fractal_hex_tile_1st.jpg

$16 Cubes, fractal hexagonal tiling$
12_Cubes_fractal_hex_tile_2nd_o4.jpg
12_Cubes_fractal_hex_tile_2nd.jpg
2500x2400 px.

$144 Cubes, fractal hexagonal tiling$
144_Cubes_fractal_hex_tile_3rd_o16.jpg
144_Cubes_fractal_hex_tile_3rd_o4.jpg
2000x2100 px.
144_Cubes_fractal_hex_tile_4th.jpg
12 MB, 8000x8700 px.
This figure is composed of all rotations (3x8 corners), including mirroring (x2) and rotated shadowings (x3), of the same cube.

$1728 Cubes, fractal hexagonal tiling$

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Comments are welcome (dow[at]uoregon.edu).