Fold
The bench for the fold itself. Load your own images or work with the house set, then vary the three parameters that decide how the piece behaves — how many images it carries, how steeply it is folded, and how finely it is cut.
Plates
Using the house set — load your own to replace any of them
Plate 1 · comes square at -45°
Seen when you stand to the left of the piece.
Plate 2 · comes square at +45°
Contrast with the others in colour and composition.
Parameters
Each image at its own station
- Image 1-45°100% clean
- Image 2+45°100% clean
“Clean” is the share of what you see that belongs to the intended image. Two plates at 45° or steeper reach 100% — the other facet is exactly edge-on and contributes nothing. Drop the fold angle below 45° and even two plates begin to contaminate each other, which is why 45° is the canonical angle rather than a matter of taste.
Cutting, for a 200 mm piece
- Strip widths
- 5.05 · 5.05 mm
- Fold depth
- 3.57 mm
- Flat sheet
- 283 mm wide
- Creases
- 55 · 28M / 27V
Why two images is the honest limit
Spread the facet angles evenly across [−θ, +θ]. Two plates give ±θ, the triangular wave. Three give +θ, 0, −θ — a trapezoidal wave whose middle facet faces straight ahead. A facet running at angle α is square to a viewer standing at −α, so the images arrive across the arc in turn.
The profile closes on itself for nothing: the angles are symmetric about zero and the tangent is an odd function, so with equal horizontal runs the rises cancel in pairs and the sheet returns to its starting depth every period. That is what keeps this foldable from one flat sheet at any plate count.
What does not scale is the separation. A facet is visible from anywhere within 90° of its normal, so two orientations can sit exactly 90° apart and each vanishes at the other's station — and three inside a 180° arc cannot. For two plates the contamination is cos 2θ clamped at zero, reaching nothing at exactly θ = 45°. That is why 45° is the canonical fold angle: the shallowest that separates two images completely.
What the sheet costs
Beyond two plates the strips stop being equal, and the result is counterintuitive: a middle facet lying flat is not foreshortened at all, so a three-plate fold at 45° fits on a narrower sheet than a two-plate one. Adding an image can cost less paper. It costs more creases instead — one per facet rather than one per pair, all but one of them mountains, since walking a period the slope only ever decreases. Take the numbers above to the Interlacer to get the sheet itself.