Sixteen hundred squares, each turned by a sine plus a cosine of its own row and column.
A heading per cell
Every square in the field is drawn by the same virtual turtle walking the same
five-segment path — half a step in, three sides, half a step out. The only thing that
varies from cell to cell is the heading it sets before starting.
That heading is a sum of two waves in the cell’s row and column indices: a sine of one
and a cosine of the other. No state is carried between cells, and nothing is random.
A fifth of the field.
Why bands appear
Two fifths. Neighbouring squares differ by a small amount, so the field reads as a
continuous surface rather than as a scatter — the same reason a noise field looks like
terrain.
Three fifths. The bands are the interference between the two waves: they run along the
curves where the sine and the cosine reinforce, and they fade where the two cancel.
Because the two waves are in different variables, those curves are not straight, and the
field acquires a swirl that neither wave has on its own.
Four fifths. There is a second interference on top of the first, and it belongs to the
square rather than to the waves: a square looks the same under a quarter turn, so the
visible angle is the heading modulo 90°. Where the heading passes through a right
angle the pattern appears to reset, and the resulting contour lines are a moiré between
the wave and the tile’s own symmetry.
The full field: forty squares a side.
Colour renderings
| Rendering | Grid | Wave character | Ink |
|---|
| Warp Cyan | 40×40 | balanced | cyan on black |
| Warp Magenta | 35×35 | balanced | magenta on near-black |
| Warp Lime | 25×25 | slow, spacious | lime on dark |
| Warp Amber | 55×55 | rolling, directional | amber on near-black |
| Warp White | 65×65 | fine, many ripples | near-white on black |
Wave frequency and amplitude decide the composition — a small change to either moves the
bands across the whole field, because the pattern is an interference rather than a
drawing. Varying those parameters alongside grid density produces renderings that are
structurally as well as visually distinct.
Museum presentation
Museum Cyan is a gallery-ready framing of the lead rendering, drawn by the
MuseumFrame presentation layer from SkiaSharp.Extensions. The forty-by-forty field
is contain-fitted into an opening behind a mat, inside a dark frame, hung on a gallery
wall with a soft drop shadow; any bleed is clipped at the mat edge like a print behind
glass. The generative parameters are identical to Warp Cyan. The framing layer is
separate from the wave-rotation logic, so the same treatment can be applied to any
rendering without altering the underlying piece.
Determinism
Nothing is seeded and nothing is random. Every heading is a closed-form function of two
integers.
