Complex parametric curves

Scripting
f(x)=sin(x)+cos(x^2)[br]#exp( ί * theta * x)= (cos(theta ))^x + ί (sin(theta ))^x[br]theta = Slider(0, 5, 0.01, 1, 140, false, true, false, false)[br]Re(x) = real( ℯ^( ί * theta * x)) * f(x)[br]Im(x) = imaginary(ℯ^( ί * theta * x)) * f(x)[br][br]a=-pi[br]b=pi[br][br]curve=Curve(t, Im(t), Re(t), t, a, b)[br][br]eps = 0.05[br]Segmts = Sequence(Segment((i, 0, 0), curve(i)), i, a, b, eps)[br][br]n=Slider(0, 150, 1, 1, 140, false, true, false, false)[br]SetValue(n, 150)[br]Execute(Sequence("A"+i+"=Segment((a+(b-a)*"+i+"/n, 0, 0), curve((a+(b-a)*"+i+"/n)))", i, 1, n))[br][br]Execute(Sequence("ShowLabel(A"+i+", false)", i, 1, n))[br][br]Execute(Sequence("SetDynamicColor(A"+i+", "+i+"/n, 0.38, 0.99)", i, 1, n))[br][br]faces=Slider(0, 4, 1, 1, 100, false, true, false, false)[br]u_1=(1,0,0)[br]u_2=(0,1,0)[br]u_3=(0,0,1)[br]u_4=(1;120°;-20°)[br]listvectordirection={u_1,u_2,u_3,u_4}[br]Selectedvector=Element(listvectordirection, faces)

Information: Complex parametric curves