Enzymind Labs

Triangles of corners:

A 2x2x2 many symbol replacement pattern. This pattern was a result of trying to engineer a recursive replacement system to produce a tetrahedron. If the system does not act uniformly on a face, a fractal pattern like this is bound to occur.

Large versions, to 2300 x 2000 px.

Space Software was used to render one face (below) of Ver7-2x2x2_21s--7g.vol (see attached, and a link to the code in notes below). The full pattern is formed of these trianglular patterns, rendered with rotated lighting at 2*pi/3 intervals, flipped and mirrored for the six triangles. There are no cues that indicate whether the "corner" texture features are concave or convex, and the lighting direction is ambiguous and different for each of the six triangles.

One face of the tetrahedral pattern.

Rendering of the full tetrahedral pattern. Stereo pair, cross-view.

Notes on Triangles of corners construction and rendering:

To generate the raw volume:

Matlab command:
(This command writes a Space Software Type 1 volume to the current directory)
>> L_System_3D_tiling( 'Ver7', 7, 21, 1, 0, '', 1, [ 0 0; 0 0], [ 0 0; 0 0], [ 6 2; 3 7], [ 4 8; 9 5], [ 6 2; 12 7], [10 8; 20 11], [ 6 12; 3 7], [13 20; 9 15], [ 6 10; 13 20], [ 4 8; 9 14], [20 11; 15 7], [14 8; 9 5], [ 0 0; 0 6], [ 0 6; 6 20], [ 7 0; 0 0], [20 7; 7 0], [ 8 0; 20 8], [ 0 0; 8 0], [ 9 20; 0 9], [ 0 9; 0 0], [ 6 10; 20 20], [10 8; 20 20], [20 11; 20 7], [20 8; 20 11], [ 6 12; 12 7], [20 20; 20 20], [ 6 20; 13 20], [13 20; 9 20], [20 20; 20 20], [14 8; 9 14], [20 20; 15 7], [20 20; 9 15], [ 0 16; 16 16], [16 16; 16 20], [17 17; 17 0], [20 17; 17 17], [18 18; 20 18], [18 0; 18 18], [19 20; 19 19], [19 19; 0 19], [20 20; 20 20], [20 20; 20 20] );

[16-19th rules not used]

Numbering system for rules.

The rule system is clunky in this form -- there are rules needed for each corner and edge of a tetrahedron, and more than one rule for each tetrahedral face.

Rule 0 is transparent in rendering.

Rule 1 is the initial symbol, the four vertices of a tetrahedron, with respect to the cubic rules.

Rule 20 is a terminating rule, the interior (white) symbol.

[ To Do: Outline and illustrate the rule system ]

(also see Tetrahedron_system.txt)

Rendering notes

In Space Software: 

Edit corners to be same color as edge.

Select face with darkest tracing voxels, View |Slice Position:

theta = -225
phi = -35.265
z = -220

Oversample (Volume | Resize) to 512³

Render parameters:

Render off window

negative edges off

Smoothing scale = 1.0

Fade with depth off

Ray trace, no shadowing

Lighting: LR +-.72, 1.0, 1.0 and 1.0, +-.1, 1.0 and +-.45, 1.0, 1.0 (these should have been normalized to 1.)

Specularity = 3

Magnification = 2

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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.