Bogen pattern cobblestone paving

"... The second type of incremental scales has a reference, where a reference position is aligned with on increment of the incremental scale.
Typically, motion control systems are based on incremental systems. They provide a relative movement scheme as input. Incremental systems will require a home run to find the reference position and then count from there...

There are many possible solutions for absolute measurement. BOGEN can produce scales for any absolute pattern and provides several different types of sensing heads for some of the technologies. ...Using a binary patterns, multiple tracks can be written in parallel. Through the binary system using the zero as a north pole and the one as south pole, a magnetic pattern can be written, where each combination of the different tracks provides one position... "
http://www.bogen-electronic.com/en/magnetic-measurement-solutions/technology/absolute-and-incremental-measurement.html


Conformal cobblestones open ended question:
"Conformal mappings make a good basis for such patterns because of their angle-preserving property, which means that a square grid is mapped onto a curvilinear orthogonal grid which can be easily constructed from an arrangement of square cobblestones (setts).
The curves in the Bogen pattern are catenaries of equal strength. They are described by ξ=c−lncosη
and ξ=c−lnsinη, where f(z)=ξ+iη and c is a real constant.
Other conformal mapping functions commonly seen in cobblestones are f(z)=z
(rectilinear) and f(z)=ez

(circular). But which other functions would be suitable, and which have actually been used?
[Edit: function definitions inverted to conform to usual convention.]

complex-analysis conformal-geometry"

https://math.stackexchange.com/questions/948043/conformal-cobblestones