In my personal research project, I've generated the below graph using the following equation:
$$D(z)=\frac{1}{2^z}-2\bigg\lfloor\frac{1}{2^{z+1}}\bigg\rfloor$$
Where $z=a+bi$, with the hue of the graph corresponding to the value of $b$ and the brightness corresponding to the value of $a$.
This equation uses the following extension of the floor function to the complex numbers as:
$$\lfloor a+bi\rfloor=\lfloor a\rfloor+\lfloor b\rfloor i$$
I've rotated the original image 90 degrees clockwise to highlight the curve in question in a better orientation.
I've been able to deduce with reasonable certainty that the graph has main features that have a period of $\frac{\pi}{\ln(2)}$. I'm curious to what equation would best fit the largest black curve within the red lines. My first guess failed as it would seem that neither the shape of $\sec$ nor $\sec^2$ (scaled accordingly) fits. I apologize for my lack of proper preparation as I have not double checked if the horizontal axis in the image is at the correct altitude. I'm not a professionally trained mathematician in any regard.
I'm grateful for any suggestion or insight.
Your discontinuities in intensity occur when the real part of
$$\frac1{2^{z+1}}$$ crosses an integer, i.e.
$$e^{-z\log2}=\frac{\cos(y\log 2)}{2^x}=2n$$