Parameter journeys — one value, many connected views

A parameter journey shows how an idea behaves across a family of cases. Instead of rebuilding the scene for “negative”, “zero”, and “positive”, declare one visible value, connect it to the existing world once, and animate only that value.

parameter(a, (cx, 140), -1.2, -1.5, 1.5, "a", 2);

plot(curve, (cx, 720), 110, 58, "x*x", (-3.3,3.3));
circle(point, (cx, 1200), 22);
counter(magnitude, (cx, 1360), 0, 2, "a² = ", "");

bind(a, curve, formula, "0.22*p*x*x");
bind(a, point, x, w*0.18, w*0.82);
bind(a, point, scale, "0.78+0.22*abs(p)");
bind(a, magnitude, value, "p*p");

step("flatten") {
  to(a, value, 0, 2.2, smooth);
}
step("opens-up") {
  to(a, value, 1.25, 2.4, smooth);
}

The plot, point, scale, number, and native parameter control move on the same continuous clock. Nothing is replaced and no scene construction is duplicated.

The three-part mental model

This pattern is domain-neutral. The parameter can be a quadratic coefficient, damping factor in a formula plot, probability, sample-size readout, geometric position, opacity comparison, colour phase, or any other scalar that makes the idea easier to see.

Declare the visible parameter

parameter(id, (x,y), initial, min, max, ["label"], [decimals]);

parameter produces a typeset numeric readout and a compact track/dot widget. The initial value must be inside a finite min..max range. Animated values are clamped to that range, which prevents an accidental journey from leaving the meaningful domain.

The whole widget is tagged id.widget, so it can enter with the rest of the story:

hidden(a.widget);
show(a.widget, 0.4);

It is an authored animation control, not an interactive slider in the exported video. Use ordinary to to move it; stateless evaluation keeps preview seeking and recording deterministic.

Connect with a responsive range

The simplest binding maps the parameter’s declared minimum and maximum onto two output values:

bind(a, point, x, w*0.18, w*0.82);
bind(a, label, opacity, 0.25, 1);
bind(a, arrow, angle, -25, 25);

This form is especially useful for positions because the endpoints are normal Manic expressions. w, h, cx, and cy are evaluated before the binding is created, so the same source can give each output format an appropriate range.

Connect with a formula

Use a string formula for a nonlinear relationship:

bind(a, point, scale, "0.8+0.2*abs(p)");
bind(a, result, value, "p*p");
bind(damping, wave, formula, "exp(-p*abs(x))*cos(4*x)");

Inside a binding formula, p is the live parameter. A plot-formula binding also provides x as the plot coordinate. The usual arithmetic, constants, and functions—sin, cos, exp, sqrt, abs, round, and others—work here.

Bindable properties are x, y, opacity, scale, angle, hue, value, trace, and a plot’s formula. A value target must be a counter. A formula target must be a plot.

When a plot formula changes, its existing tangent, normal, slope, area, integral, and moving mark views receive the new function before they recompute. That is the important reactive promise: the analysis stays mathematically tied to the curve the viewer sees.

Choose cases, not frames

Use named steps to describe meaningful cases:

step("underdamped") {
  to(damping, value, 0.12, 2.0, smooth);
  say(caption, "The oscillation survives for longer.", 0.35);
}
step("strong-damping") {
  to(damping, value, 0.85, 2.0, smooth);
  say(caption, "The same response now settles quickly.", 0.35);
}

The stage names should explain the cases to a human. The parameter supplies the continuous motion between them; bind keeps every connected view synchronized.

Creator design tips

• Follow one primary parameter per short scene. Several controls are possible, but the audience should know which value is changing.
• Connect two or three complementary representations—a formula and plot, a geometry and measurement, or a simulation curve and readout.
• Give the parameter a meaningful range. Avoid travelling through singular or irrelevant values merely because the engine allows them.
• Use responsive range bindings for positions and formula bindings for meaning.
• Hold the important cases briefly. Smooth motion reveals the trend; the hold lets the viewer name it.
• Keep stable ids. Parameter journeys are an extension of the persistent-world model, not a reason to create replacement scenes.
• Run manic check FILE.manic --canvas all after the journey is complete.

Complete example

Parameter journeys is the polished reference: one coefficient drives a quadratic, live tangent and slope, moving point, changing scale, and a² readout across portrait, feed, square, and landscape.

Current bindings target 2D entity properties and formula plots. Constructors that perform expensive build-time work—such as re-simulating a full physics system or changing the number of generated objects—remain build-time choices; represent those journeys with a formula/readout today rather than implying that Manic silently recomputed the model.

Next: Meet the shapes that make up the persistent world →