Don't quite understand how your tangent example fits in with the z_n+1 = f(n, z_n) idea HG?

Here's a subprogram I wrote in BASIC to generate the classic Mandelbrot set z->z^2 + C

Private Sub Command1_Click()
Dim counter As Integer
Dim a As Double, b As Double, c As Double, d As Double
Rem z = a + ib
Dim creal As Double, cimag As Double
Rem c is the complex add-on point
a = 0: b = 0: c = 0: d = 0
Open "testmand.txt" For Output As #1
For cimag = -2 To 2 Step 0.005
DoEvents
For creal = -2 To 2 Step 0.005
a = 0: b = 0: c = 0: d = 0
counter = 0
While (Abs(a + b) < 4 And counter < 200)
c = a ^ 2 - b ^ 2 + creal
d = a * b * 2 + cimag
a = c: b = d
counter = counter + 1
Wend
If (Abs(a + b) < 4) Then
Print #1, "*";
Else
Print #1, " ";
End If
Next
Print #1, " "
Next
Close #1
End
End Sub

David