Multiple plots using dynamics

Question

I am studying Dynamic and DynamicModule, and I have tried to make a simple plot of a family of real functions. The number of functions should be a dynamic variable controlled by a slider. So I have tried something like this

{Slider[Dynamic[z], {1, 4, 1}], Plot[Evaluate[Dynamic[Table[Sin[i*t], {i, 1, z}]]], {t, 0, 2 Pi}]}

In this case variable t is highlighted in red and the output is empty. But if you do it outside of Plot[], then you get a correct list of functions

{Slider[Dynamic[z], {1, 4, 1}], Evaluate[Dynamic[Table[Sin[i*t], {i, 1, z}]]]}

So, how one plots this kind of things?

Answer 1

The Plot has to be within Dynamic, as the Plot needs to be updated when z is changed. You can't just update the content of Plot without making a new Plot.

{Slider[Dynamic[z], {1, 4, 1}], 
 Dynamic@Plot[Evaluate[Table[Sin[i*t], {i, 1, z}]], {t, 0, 2 Pi}]}

The syntax highlighting is due to the Head of your command inside Plot being Dynamic

Evaluate[Dynamic[Table[Sin[i*t], {i, 1, z}]]] // Head

Dynamic