Interaction

#Parameters

A parameter is a named quantity with a slider in the environment footer. Its var is a single letter, and every expression in the environment that mentions that letter re-evaluates as the reader moves it.

canvas.graph{
    parameter#a(var: a; name: steepness; range: [0, 4]; step: 0.25; default: 2)
    curve(expression: a * x^2)
    point(x: 1; y: a; label: $a$)
}

name: is what the parameter is called in front of the reader — rich text, so Frequency $b$ sets its own maths — and without one the slider is labelled with its letter. hidden: true keeps it out of the footer — the expressions still use it, the reader cannot move it — and lock: true keeps it out of their reach on an editable environment. Its current position is derived as #a.value, readable in prose as {{#a.value}}.

#Giving fit a parameter for its degree

fit takes its degree as a number or as an expression of parameters. A parameter in that position hands the degree to the reader: the parameter's slider is the control, and the fit recomputes as it moves.

canvas.graph{
    scatter(x: 1, 2, 3, 4, 5; y: 2.0, 2.4, 3.1, 4.8, 7.4)
    parameter#d(var: d; name: fit degree; range: [1, 4]; step: 1; default: 1)
    fit#f(model: polynomial; degree: d)
}

#f.slope, #f.intercept and #f.r2 are derived from whatever the reader has chosen, so prose that reads them stays true at every degree.

#editable: environments and lock:

editable: true on a canvas.graph lets the reader add their own elements and pan or zoom the frame; on a canvas.code it lets them edit the text, which still runs nothing. Any mark takes lock: true to stay out of their reach — and does nothing at all on an environment that is not editable.

#continue: and session state

A later environment written as continue: #projectile inherits what the reader did in the earlier one: where they left the sliders, the degree they chose, the view they zoomed to. Only that state carries — the content is the new environment's own.