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Flattum Center for Kinetic Research

Parallax geometry · Kinetic form

Lenticular

Same interlacing, different selector. A fold chooses by turning facets away from you. A lenticular sheet lays a row of cylindrical lenses over a flat print, and each lens magnifies whichever strip sits under its focal point. Nothing is ever hidden, only unmagnified — which is why a lenticular can hold a dozen images where a fold separates two.

Lens sheet

Print at this pitch, not the one on the box

59.9769 LPI

The sheet is sold as 60 LPI. Print at that nominal figure and the strips creep 0.12 mm across a 300 mm sheet — enough to slip a whole view after 138 mm, which is what a band of the wrong picture down one side of a bad lenticular actually is.

printed at the corrected pitchprinted at the pitch on the box
Viewing angle
63°
Dots per strip
2.50
Views this printer can hold
10
Moiré risk
high

Moiré is the second way these fail, and unlike the pitch it cannot be fixed after printing. When a strip does not land on a whole number of printer dots the rounding error repeats, beating slowly against the lens pitch — here each strip is 2.50 dots, 0.50 away from whole.

The pitch is not the pitch

Rays from a viewer at a finite distance fan outward, so a lens at the edge of the sheet is struck at an angle while the one in the middle is struck square. For the same strip to land under every lens, the print has to be very slightly wider than the lens array:

printPitch = lensPitch · (1 + t / (n · D))

t = sheet thickness      n = refractive index (~1.56)
D = viewing distance

The correction is parts in ten thousand and completely unforgiving. It also explains something about the medium: as D grows the correction vanishes, so sheets cut for billboards are pitched almost at nominal, while anything meant to be held in the hand needs the largest correction of all.

Against the fold

Selector
Facets turn away · a lens magnifies
Images
Two, cleanly · a dozen or more
Transition
Continuous blend · a flick between views
Fails by
Ghosting between plates · pitch drift and moiré
Made with
Paper and a bone folder · a calibrated printer

The fold's limit is real — two images and no more, for reasons of geometry — but everything it needs is a sheet of paper and patience. The lens buys view count with a calibration problem, and that trade is the whole difference between the two media.