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Digital artifact 002 · Source geometry / 12grid.dxf

12-Grid
Tessellation.

Six line directions become twelve rays, building a dense field from a compact vocabulary of 30-degree turns and square-root-of-three proportions.

The viewer reconstructs the supplied CAD linework directly from its DXF source. It opens inside the pattern rather than outside it: drag to travel, magnify the local weave, isolate the directional families, or step back to inspect the complete source frame.

5,044 tessellation lines06 / 12 axes / rays64 translated cells
Interactive twelve-grid tessellation Exact line entities parsed from the supplied DXF and grouped into six directional families at thirty-degree intervals.
Reading the CAD field…
Local weave2.65× magnification

Drag the field to travel through the drawing.

Read the field

01 / Directional grammar

Six axes.
Twelve rays.

Every measured segment aligns to one of six undirected orientations: 0°, 30°, 60°, 90°, 120°, or 150°. Read in both directions, those axes form a twelve-ray compass.

That distinction matters. The drawing uses a dodecagonal directional vocabulary, but its 8-by-8 crop and translated cells do not make the entire composition a single globally twelvefold-symmetric object. Local order and global framing coexist.

Twelve rays spaced by thirty degrees
Angular interval30°360° / 12 rays
Drawing extent8 × 8source units
Unit translations8 × 864 repeated cells
Common signatures60segments recurring in every cell
Direction interval30°six axes / twelve rays

02 / Measured proportions

A field written
with √3.

The recurring lengths are not a random decimal inventory. Several resolve directly into compact expressions containing the square root of three—the metric signature expected when 30-degree and 60-degree constructions share a field.

Primary diagonal0.5773501 / √3
Half diagonal0.2886751 / (2√3)
Offset A0.366025(√3 − 1) / 2
Offset B0.133975(2 − √3) / 2
Quarter offset0.066987(2 − √3) / 4
Third offset0.211325(3 − √3) / 6

ReadingThe grid joins two familiar systems: a square translation field and 30°/60° angular construction. Their overlap naturally carries both rational halves and irrational √3 offsets.

64-cell translation field

03 / Source audit

Repetition with
CAD fingerprints.

The file contains 5,048 LINE entities: 5,044 on the tessellation layer and four on a separate framing layer.

108distinct segment signaturesafter translation-normalizing the 8-by-8 field

60signatures repeat 64 timesone occurrence in every unit cell

256near-zero micro-seams0.00004 source units each; preserved in Source mode

Those micro-seams are only one twenty-five-thousandth of a unit edge. The default weave suppresses them for a cleaner screen reading; Source mode restores them and the four-line frame without assigning them a meaning the file itself cannot prove.

04 / Translation

Zoom past
the boundary.

The drawing is most atmospheric when the full extent disappears. Enlarged fragments trade diagrammatic completeness for texture, directional flow, and an implied field continuing beyond the screen.

Interface

Overscaled line atmosphere

Crop the field beyond the viewport and retain only a faint subset of lines behind content, navigation, or transitions.

Fabrication

Layered engraving

Separate direction families into depth, material, or illumination channels while preserving a common registration system.

Architecture

Screen and glazing study

The unit-cell logic can inform perforated panels, etched glass, acoustic surfaces, shading screens, or luminous ceiling fields.

Motion

Counter-moving families

Opposed axes can drift at different rates so the pattern appears to breathe without losing its geometric register.

Artifact statusExact DXF parsed · mathematical reading active

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