Q: Why curvy PCB traces?

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At first I thought the width of the trace varied smoothly. This is to prevent signal reflections from changes in impedance.

But what I see here looks like you have high-speed digital signals going down these traces, and they all need to arrive at the same time. So, if some paths would be shorter than others, you curve them around so they all line up in the end.
 
Heavyweight PCB CAD packages can do that automatically: Nets can be tagged / paired as requiring equal path lengths and an 'autorouter' will push and shove other traces out of the way to make the space.

This is often seen with high speed pairs into differential line receivers.
 
Skew control, have a look at the requirements for DDR memory, one of the more critical interfaces on a PCB. It requires a router that can handle high speed designs, you have to enter the max skew as either a time or a length. It cannot usually be done manually as quite often you are matching signals within one group to signals within other groups and then to clocks. To make matters worse, when this is on a board the board quite often has to be impedance matched, so each signal layer has to be closely tied to a ground plane for return currents.
Its most noticable on mother boards between the CPU, interface chips and the DDR sockets.
 
No is the short answer, its more prone to artifacts such as mutual crosstalk, the general rule being use 3 tiems the track to track spacing between the consatinas where possible. If you want to create inductors on a PCB look up "planar transformers", you can do all sorts of funky things.
I'd say the pattern on that PCB would create more capacitive coupling between the planes than inductive.
Rememeber it is signal rise times that cause signal integrity problems, use the slowest possible rise time for any signals to minimise problems.
 
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