I'd like to pass functions / expressions into Manipulate[ComplexPlot[...]...] and have Manipulate update some of the values and then update the plot correspondingly.
For instance:
In[161]:= ClearAll[f, n]
In[172]:= f[z_] := z^n
In[174]:= n = 2
Out[174]= 2
In[175]:= f[I]
Out[175]= -1
In[176]:= f[z]
Out[176]= z^2
In[177]:= Manipulate[ ComplexPlot[f[z], {z, -(2 + 2 I), (2 + 2 I)}], {n, 1, 5}]
The above makes a nice colorful plot with a slider to change the value of n, but when I move the sider the plot does not update... [see image below]
OTOH:
Manipulate[ComplexPlot[z^n, {z, -(2 + 2 I), (2 + 2 I)}], {n, 1, 5}]
Makes a nice plot that updates as I move the slider.
But I want to pass in functions to ComplexPlot inside of Manipulate, so that I can define them outside of Manipulate[].
Is there an easy to understand and concise way to do this? One that doesn't involve a lot of deep knowledge of Hold, Evaluate, @, #, etc :-)
