Enzymind Labs

[ To Do: More documentation and material planned.]

Tetrahedral alternating, 0_2000_2280

The rule system alternates between the two tetrahedral 2x2x2 rules, with a terminating symbol off the tetrahedra:

All of the orthogonal (face-on) projections are filled with no occlusion; the number of elements matches the 2-D dimension product (2^n_g x 2^n_g) and the coordinate triplets cover all unique coordinate pairs. Are there other sets that have this property?

The pi/4 rotated projections are transparent, a fractal curve with a dimension between one and two that bounds a single fractal prototile.

[ To Do: Compare this with the Serpinski sponge, 2 symbol with no alternation. ]

The fifth generation (32 x 32 x 32), rendered with darker shades at increasing depth.
(stereo pair, cross view)

Larger versions
(stereo pair, cross view)
The seventh generation (128 x 128 x 128), rendered with darker shades at increasing depth.

Large version
Rendered animated rotation of the system's fifth generation cube, between adjacent faces of of the volumetric cube. A larger animation of the system's seventh generation.

Same 2-D + time animation as above, but skewed in space-time (Euler angles pi/6 radians).

The second generation, oversampled by x3 and sliced and volume rendered along the long diagonal. The apparent layering is due to flaws in the Space Software rendering engine with small volumes (24³ voxels in this case). An MP4 format movie of this figure: Altered_tetrahedron_sliced.mp4.

Matlab command:
>> volOut = L_System_3D_tiling( '', [n_g], 3, 1, 0, '', 1, [0 0; 0 0], [0 0; 0 0], [0 2; 2 0], [2 0; 0 2], [1 0; 0 1], [0 1; 1 0] );
where [n_g] is the number of generations.
The raw seventh generation volume: LS-2x2x2_3s-0_2000_2280-7g.vol.gz. Oversampled and rendered with Space Software.

Right triangular pyramid alternating, 0_6372_94

Maximum intensity projection (MIP) of the seventh generation rendered in the long diagonal direction:

Large version

This projection forms a motif for a rectangular tiling with a single fractal prototile.

Matlab command:
>> volOut = L_System_3D_tiling( '', [n_g], 3, 1, 0, '', 1, [0 0; 0 0], [0 0; 0 0], [0 2; 2 2], [2 2; 2 2], [1 1; 1 1], [1 1; 1 0] );
where [n_g] is the number of generations.
The raw seventh generation volume: LS-2x2x2_3s-0_2186_3279-7g.vol.gz is attached below. Oversampled and rendered with Space Software.

------------------------
Terms for use: There are no restrictions on the use of these images. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to dow[at]uoregon.edu, and credit are appreciated but not required.