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Manipulate

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Manipulate[expr, {u, umin, umax}, ...]

Opens an interactive window with one control per variable and re-evaluates expr with each variable bound to its current value whenever a control changes. Returns Null once the window is closed. expr is typically a Graphics[...] or Plot[...] call that depends on the control variables. Unlike Animate, every control is independently user-driven from the first frame -- there is no animation phase or playback transport. Control specs (any number, one row each): {u, umin, umax} continuous slider, default = umin {u, umin, umax, du} continuous slider with step du {{u, u0}, umin, umax} continuous slider, explicit default u0 {{u, u0}, umin, umax, du} continuous slider, default + step {u, {v1, v2, ...}} discrete button set, default = v1 {{u, u0}, {v1, v2, ...}} discrete button set, explicit default u0 Click-drag a slider handle or click a discrete button to change its value; click Reset to restore every control to its default. Esc closes the window.

Examples (5)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (4)

In[1]:= Manipulate[Plot[Sin[n x], {x, 0, 2 Pi}], {n, 1, 5}]
Out[1]= Manipulate[Plot[Sin[n x], {x, 0, 2 Pi}], {n, 1, 5}]

In[2]:= Manipulate[Plot[f, {x, -5, 5}], {f, {Sin[x], Cos[x], x^2}}]
Out[2]= Manipulate[Plot[f, {x, -5, 5}], {f, {Sin[x], Cos[x], x^2}}]

In[3]:= Manipulate[Plot[a Sin[x] + b, {x, 0, 2 Pi}], {a, 0, 3}, {b, {-1, 0, 1}}]
Out[3]= Manipulate[Plot[a Sin[x] + b, {x, 0, 2 Pi}], {a, 0, 3}, {b, {-1, 0, 1}}]

In[4]:= Manipulate[Plot3D[Sin[x + n] Cos[y], {x, -3, 3}, {y, -3, 3}], {n, 0, 3}]
Out[4]= Manipulate[Plot3D[Sin[x + n] Cos[y], {x, -3, 3}, {y, -3, 3}], {n, 0, 3}]

Options (1)

In[5]:= Manipulate[ Graphics[Disk[{0, 0}, r], PlotRange -> {{-5, 5}, {-5, 5}}], {{r, 2}, 0.5, 5, 0.25}]
Out[5]= Manipulate[-Graphics-, {{r, 2}, 0.5, 5, 0.25}]

Algorithm

manipulate.c — Manipulate[expr, {u, umin, umax}, ...]

Opens a Raylib window (when USE_GRAPHICS is compiled in) with one control row per variable, stacked above a thin footer:

  ┌─────────────────────────────────────────────────────────────┐
  │                                                               │
  │                        (rendered content)                    │
  │                                                               │
  ├─────────────────────────────────────────────────────────────┤
  │ u  │ 0 ─────────────●────────── 10              │  3.42     │
  │ f  │ [Sin[x]] [Cos[x]] [Tan[x]]                              │
  ├─────────────────────────────────────────────────────────────┤
  │ [Reset]  Esc: close                                          │
  └─────────────────────────────────────────────────────────────┘

Each control is independently user-driven from the first frame — there is no animation phase or playback transport (see Animate for that). A control is either:

  - a continuous drag slider:  {u, umin, umax}, {u, umin, umax, du},
    {{u, u0}, umin, umax}, {{u, u0}, umin, umax, du}
  - a discrete button set:     {u, {v1, v2, ...}}, {{u, u0}, {v1, ...}}

Implementation notes

Attributes: HoldAll, Protected.

References

See also: HoldAll, Animate, Show