Technical data for this type of fractal : click here (JMC-A01-01).

Parameters used here :
fn1() = cos(), fn2() = atanh()
real(p1) = 1, imag(p1) = 4, real(p2) = 0.5, imag(p2) = 0.5, real(p3) = 0, imag(p3) = 0
Note.
A zoom on the center of this fractal will always gives the same image no matter the number of zooms.

Below two images of the same fractal with colorful palettes of colors.
For each of these two factals, a zoom on their center will always gives the same image no matter the number of zooms.





All the above images belong to an alignment of two images with a center of symmetry for the two images along the x axis.
The length of this alignment is infinite.
The center of symmetry is easy to find.



Same image after a counterclockwise rotation.



Same images with two different palettes of color.





Zoom on the center of symmetry (the small green center of the above image).