Doyle Spiral and Mobius Transformation

By Xah Lee. Date: .

Doyle spiral + Mobius transformation

math art marbles spirals-2
Doyle spiral + Mobius transform by fdecomite image source on . 2800×2100 © https://creativecommons.org/licenses/by/2.0/legalcode

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) .