Wolfram Technology Guide: Dynamic Interactivity  previous | next 
Immediately Create Complex Dynamic Graphics
Mathematica allows any parameter of any program to be manipulated interactively.
In[1]:=

Click for copyable input
Manipulate[

 Graphics[Line /@ 

    NestList[

     Flatten[# /. 

        g[a_, b_] :> (g[b, b + (b - a) #] & /@ {x + I y, 1/2, 

            x - I y})] &, g[0, 1], t] /. 

   g[a_, b_] :> {{Re[a], Im[a]}, {Re[b], Im[b]}}, PlotRange -> All, 

  ImageSize -> {500, 400}],

 {{x, 0, "horizontal offset"}, 0, 1},

 {{y, .5, "vertical offset"}, 0, 1}, Delimiter,

 {{t, 6, "number of steps"}, 1, 8, 1}]
Out[1]=