SparshaRay / Logarithmic-Fractal

A spiraling fractal on the complex plane.

Logarithmic-Fractal

A spiraling fractal on the complex plane.

The basic fractal is defined as the set Z_n as n tends to infinity, where -
Z_n+1 = { (2m + sgn(Re(z)) (1-e^{|Re(z)|(ln(k)+𝑖)}) + k^|Re(z)| e^{𝑖(|Re(z)|-arctan(ln(k))} Im(z)) | z∈Z_n, m∈ℤ } ,
Z₀ = { (2m + sgn(Re(θ)) (1-e^{|Re(θ)|(ln(k)+𝑖)}) | θ∈ℝ, m∈ℤ } ,
k ∈ (0, 1)

It is a fractal of logarithmic spirals.