# Doyle Spiral and Mobius Transformation

### Doyle spiral + Mobius transformation

can you identify what function is this?

it looks like a Mobius Transformation. But what's the exact parameters and what's the input image? (assume each ball is just a dot.)

Mobius Transformation is a function of the form `f[z] = (a z + b) / (c z + d)`

and `a d − b c ≠ 0`

. The variables are all complex numbers.

For a simple geometric explanation of complex numbers, see: Isometries: Translation, Rotation, Reflection and Mandelbrot Set Explained (no complex number needed) .