System: parametric_curve

Structural

Parameter	Default	Range	What it does	Group
sym	5	superformula 1 – 24; inert on maurer_rose, lissajous, hypotrochoid, harmonograph, torus_knot, lissajous_3d	How many lobes the figure repeats around its centre, as a whole number.	shape
palette_steps	0	0 – 16	Quantizes the palette into this many flat bands; 0 leaves it continuous.	colour
mirror_order	1	maurer_rose 1 – 12; lissajous 1 – 12; hypotrochoid 1 – 12; superformula 1 – 12; harmonograph 1 – 12; inert on torus_knot, lissajous_3d	Repeats a flat figure this many times around the centre; 1 draws it once.	shape

Modal

Parameter	Default	Range	What it does	Group
n	6	maurer_rose 1 – 24; lissajous 1 – 12; hypotrochoid -8 – 8; harmonograph 1 – 12; torus_knot 1 – 12; lissajous_3d 1 – 12; inert on superformula	The figure’s first number, read as a real value per family: the rose’s petal number, the two Lissajous figures’ and the harmonograph’s x frequency, the hypotrochoid’s signed radius ratio, the knot’s whole turns round its axis.	shape, main
d	71	maurer_rose 1 – 360; lissajous 1 – 12; hypotrochoid 1 – 24; superformula 0.25 – 4; harmonograph 1 – 12; torus_knot 1 – 12; lissajous_3d 1 – 12	The figure’s second number, per family: the rose’s sampling step in degrees, the two Lissajous figures’ and the harmonograph’s y frequency, the hypotrochoid’s cusp count, the superformula’s lobe skew, the knot’s whole turns through its hole.	shape, main
phase	0	maurer_rose 0 – 1; lissajous 0 – 1; hypotrochoid 0 – 1; harmonograph 0 – 1; lissajous_3d 0 – 1; inert on superformula, torus_knot	Offsets where the figure starts: inside the rose’s sine, between the two Lissajous figures’ and the harmonograph’s x and y axes, and at the hypotrochoid’s pen.	motion
radial_offset	0	maurer_rose -1 – 1; inert on lissajous, hypotrochoid, superformula, harmonograph, torus_knot, lissajous_3d	Pushes every point out from the centre, opening the figure into a ring.	shape
pen	1	hypotrochoid 0 – 2; inert on maurer_rose, lissajous, superformula, harmonograph, torus_knot, lissajous_3d	How far the tracing point sits from the rolling circle’s centre, in rolling radii: 1 draws cusps, less rounds them off, more throws them into loops.	shape
sharpness	1	superformula 0.1 – 20; inert on maurer_rose, lissajous, hypotrochoid, harmonograph, torus_knot, lissajous_3d	How pointed the lobes are: low draws a spiky star, high rounds the figure toward a circle.	shape
lobe	1	superformula 0.1 – 10; inert on maurer_rose, lissajous, hypotrochoid, harmonograph, torus_knot, lissajous_3d	How the lobes swell between their tips: low pinches them thin, high fills them into a polygon.	shape
decay	0.1	harmonograph 0 – 0.5; inert on maurer_rose, lissajous, hypotrochoid, superformula, torus_knot, lissajous_3d	How fast the pendulums die away along the trace: 0 closes the figure, more spirals it inward.	light
tube	0.4	torus_knot 0.05 – 0.9; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph, lissajous_3d	How far a knot’s strand winds out from the torus’s core circle, as a fraction of that circle’s radius.	shape
m	1	lissajous_3d 0 – 12; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph, torus_knot	The depth axis’s frequency on a 3D Lissajous figure; 0 with phase_z at 0 lays it flat.	shape
phase_z	0.25	lissajous_3d 0 – 1; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph, torus_knot	Offsets the depth axis of a 3D Lissajous figure against the other two, as a fraction of a turn.	motion
samples	361	16 – 2048	How many points the curve is drawn from; fewer reads as a polygon. Truncated, so a rise adds its next point on arrival.	shape
thickness	2	0.5 – 12	Stroke width in pixels at the render target, before softness widens the falloff.	shape, main
hue	0.6	0 – 1	Where this scene reads from the palette, as a coordinate along it rather than a colour.	colour, main
hue_spread	0	0 – 1	How far along the palette the colour travels from one end of the figure to the other.	colour
saturation	1	0 – 1	Pulls the scene’s colour toward grey; 0 is fully desaturated, 1 is the palette’s own.	colour
palette_mix	0	0 – 1	Crossfades from the preset’s palette to its second one; 0 is the first, 1 the second.	colour
palette_contour	0	0 – 1	Draws a line at each band edge when the palette is stepped; 0 draws none.	colour
spin	0.1	maurer_rose -2 – 2; lissajous -2 – 2; hypotrochoid -2 – 2; superformula -2 – 2; harmonograph -2 – 2; inert on torus_knot, lissajous_3d	Turns per second the whole figure rotates by.	motion, main
scale	0.9	0.1 – 2	Size of the figure within the frame, before the shared zoom is applied.	shape
brightness	1	0 – 2	The scene’s overall light level, multiplying what it draws before the composite.	light, main
glow	1	0 – 4	Brightness of the halo around each stroke, on top of the stroke itself.	light, main
softness	0.25	0 – 1	How far a stroke’s edge fades out; 0 is a hard line, 1 a wide glow with no core.	light
stroke_blend	0	maurer_rose 0 – 1; lissajous 0 – 1; hypotrochoid 0 – 1; superformula 0 – 1; harmonograph 0 – 1; inert on torus_knot, lissajous_3d	Moves a flat figure’s stroke from additive light toward opaque paint, so crossings stop brightening.	light
draw_progress	1	0 – 1	How much of the figure is drawn, from its start; below 1 the line is still arriving.	motion
zoom	1	0.25 – 4	Scales the whole scene about its centre; above 1 fills more of the frame.	shape
pan_x	0		Slides the whole scene sideways, in the scene’s own units rather than pixels.	shape
pan_y	0		Slides the whole scene vertically, in the scene’s own units rather than pixels.	shape
mirror_reflect	0	maurer_rose 0 – 1; lissajous 0 – 1; hypotrochoid 0 – 1; superformula 0 – 1; harmonograph 0 – 1; inert on torus_knot, lissajous_3d	Alternates a flat figure’s repeats into mirror images rather than plain rotations.	shape
yaw	0	torus_knot -3.1415927 – 3.1415927; lissajous_3d -3.1415927 – 3.1415927; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	Turns the camera around a space curve, in radians; bind it to a slow clock to orbit.	motion
pitch	0.25	torus_knot -1.55 – 1.55; lissajous_3d -1.55 – 1.55; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	Raises the camera above a space curve, in radians; negative looks up from below.	motion
distance	3.5	torus_knot 1.5 – 8; lissajous_3d 1.5 – 8; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	How far the camera sits from a space curve’s centre; nearer exaggerates the perspective.	motion
fov	0.8	torus_knot 0.2 – 2; lissajous_3d 0.2 – 2; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	The camera’s vertical field of view onto a space curve, in radians; zoom divides it.	motion
focus	0.5	torus_knot 0 – 1; lissajous_3d 0 – 1; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	Where the focal plane sits in a space curve’s depth: 0 at its nearest point, 1 at its farthest.	light, main
aperture	0	torus_knot 0 – 24; lissajous_3d 0 – 24; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	The blur of a space curve’s far side, in pixels; strokes nearer than the focal plane blur more, up to the tier’s cap. 0 keeps every stroke sharp, and wider costs fill.	light, main
fog	0	torus_knot 0 – 1; lissajous_3d 0 – 1; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	Fades a space curve toward black with depth: at 1 its farthest point is black and its nearest keeps its light. 0 is off.	light
solid	0	torus_knot 0 – 1; lissajous_3d 0 – 1; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	1 paints a space curve’s near strands over its far ones, so it reads as an object and crossings stop brightening; 0 is the additive glow. Solid sorts every chord by depth each frame.	light
hue_axis	0	torus_knot 0 – 1; lissajous_3d 0 – 1; inert on maurer_rose, lissajous, hypotrochoid, superformula, harmonograph	Moves a space curve’s colour from running along its path (0) to running with depth (1), nearest first; between mixes the two.	colour