The [field] table

An analytic_field preset draws one closed-form function of position across the whole frame — no state between frames, nothing accumulated, the picture a pure function of this frame’s bindings. [field] picks which function:

system = "analytic_field"

[field]
family = "escape_time"   # "chladni" or "escape_time"; any other name is a load error
map    = "julia"         # escape_time only: "julia" (the default) or "mandelbrot"
trap   = "cross"         # escape_time only: "none" (the default), "point", "line", "cross", "circle"

All three keys are read once, at load, and are not bindable. A preset with no [field] table draws the Chladni plate. map or trap on the chladni family is a load error rather than a silent no-op — the plate has no orbit for either to act on.

The two families share one parameter surface, following ADR-0180: every parameter below is read by one family only and does nothing on the other. The colour and framing parameters — color_span, color_center, brightness, hue, zoom, pan_* and the shared palette block — read the same on both.

family	The figure	Structural	Modal
chladni	The nodal lines of a square plate: the zero set of cos(n π x) cos(m π y) − cos(m π x) cos(n π y)	mode_n, mode_m	line_width, plate_mix
escape_time	z → z^power + c iterated to an escape radius, coloured by the smooth iteration count	iterations	c_re, c_im, escape_radius, power, interior, trap_radius, trap_rotate

What each family does with them:

• chladni — the figure is two whole numbers. mode_n and mode_m are rounded before the plate sees them, because a fractional mode is not a standing wave of the plate at all. Equal modes cancel and the plate goes blank. The plate spans the frame’s short axis at zoom = 1 and stays square at any window shape. line_width is the band’s width in plate units, the same number of pixels wherever the lines run; plate_mix blends from the lines alone toward the whole signed wave. A mode bound to audio re-picks the figure on every frame — bind it through [hold] so it changes on the beat or the bar instead.
• escape_time — c is the lever. On the julia map, c_re and c_im are the constant, and moving c from inside the Mandelbrot set to outside it takes the figure from one connected piece to scattered dust — a bass-driven c_re does exactly that on the music. On the mandelbrot map the pixel is c and both are inert. power above 2 adds lobes; a fractional power tears the figure along the negative real axis, so reach for whole numbers unless the seam is the look. interior is the light of the set itself (0 is the textbook black).
• escape_time colours continuously. The palette follows the smooth iteration count, so the boundary reads as a glow rather than as contour steps, and one iteration spans a fixed 1/32 of the palette at color_span = 1 — raising iterations never recolours a pixel that escaped early. Band it deliberately with palette_steps, as on any other system.
• A trap recolours by nearness. With a trap, a pixel takes the palette at the smallest distance its orbit came to the trap shape instead of at its escape count — which is what draws filaments, rings and stained-glass cells. Every shape sits trap_radius from the origin (the circle’s radius, the line’s offset, the point’s and the cross’s distance) and turns by trap_rotate in whole turns, which is inert on a circle. trap = "none" draws exactly the untrapped picture.

iterations is capped by the quality tier. A tier that chose the count would make one preset two different pictures, so the preset asks and the tier bounds: the Floor tier allows 64, the Rich tier 512. A preset asking within 64 renders identically on both. One asking for more is drawn at the cap and says so — the standalone prints which preset asked for how many and what it was drawn at, the same way it reports a segment cap or a tier demotion. Author against 64 unless the deep look is the point.

The range that reads for each parameter, and the family it is inert on, is printed in the analytic_field table of Parameter roster.