Mandelbrot Lambda Function Fractal

The Mandelbrot Lambda Function Fractal can be generated with the following equation, which extends the traditional equation by allowing pertubations (a+bi) and (c+di):

{Z_{n + 1} = C fn (Z_{n} + (a + bi))}^{(c + di)}

THe 'fn' can be replaced by any function, I enjoy using the following trigonometric function: None (evaluated without a function), Sin, Cos, SinH, CosH, $e^{z}$ , Ln, $2^{z}$ .

Mandelbrot Lambda Function Fractal - with Sin function lambda