
Saar of BoldPort developed an open source software for creating artistic and functional printed circuit boards, the PCBmodE:
We wanted to create circuit boards that have curvey traces, meandering paths, and multiple soldermask layers, so we developed PCBmodE (say “PCB mode”), an open source Python software that unshackle us from the constraints imposed by traditional PCB design tools. We use the power of Inkscape – the leading open source vector graphics editor — to achieve any shape imaginable. Together with our powerful back-end tools, we can manufacturable beautifully functional boards.
Via EvilMadScientist.

Too early development stage, but it looks really interesting.
If you can maintain track thickness, and use swirls to keep track lengths the same, you could make this practical when connecting high-speed BGA parts to memory / interface chips.
Then, of course, there’s pcb-etched spiral inductors, antennas, stripline circuits…
I’ve seen a number of boards recently with curvy traces – is this a new trend?
This concept has been around for ages, but is catching on due to the introduction of EDA tools with this “curvy trace” capability. There is even a “name” for it – “Topological Routing”. There is a proprietary piece of PCB layout software called TopoR by a company called Eremex (from Russia, if my whiskey-soaked memory serves)…
http://www.eremex.com
https://en.wikipedia.org/wiki/TopoR
Can I send these PCBs to SeeedStudio?
I’m 100% certain that Seeed would be able to make those PCBs without any issues.