Function for Creating Spiral Stripes with Orientation 45 Degrees to Radial?

Question

I am trying to reconstruct the spiral pattern in the depicted image for a neuroscience experiment. Basically, the pattern has the properties that:

1) Every part of the spiral has local orientation 45 degrees to radial 2) The thickness of each arm of the spiral increases in direct proportion with the radius.

Ideally I would like to be able to parametrically vary the number of arms of the spiral as needed. You can ignore the blank circle in the middle and the circular boundaries, those are very easy to add.

Does anybody know if there is a function in terms of the number of spiral arms and local orientation that would be able to reconstruct this spiral pattern? For what it's worth I'm coding in Matlab, although if someone has the mathematical formula I can implement it myself no problem.

Answer 1

Logarithmic spirals have the properties you mention. It is loxodromic, having rhumb lines at $\alpha = \pi/4$ at any radius.

Width, not thickness, is proportional to radius/ Its mesh size varies the number of spiral arms. Possible to construct in all CAS including Matlab.

$$ r = a e^{ \cot \alpha \cdot \theta }$$