After seeing this tutorial for an abstract background, I thought it would be fun to do something similar in Inkscape.
To start, let's do a Google search for a logo. I will be using a Kubuntu logo. Go ahead and save that logo somewhere on your computer.
I am going to start with the logo so I can use that for the basis of my color palette.
Drop the logo in Inscape and we will do a bitmat trace (Path>Trace Bitmap...)
Now we will create a rectangle... this will be our background. You can change Inkscape properties so the document is the size of your screen. This is not too important though since we are working with vector, we can always change the size later to fit any screen size. Once you have the rectangle created, give it a fill gradient. I like to use the colors on the logo for the gradient colors. (You can use the eye dropper tool for this)
|Layers in Normal blend mode|
On the new layer add a few simple shapes that look nice. Use a gradient fill shape; for one color, use black then use a similar color to what you already have for the other color.
|Layers in "Screen" blend|
Now create a new layer to work in and call it "Wavy Stuff" or whatever.
Using your bezier pen tool, create a couple wavy lines that overlap each other occasionally. After creating the curves, I find it helpful to press Ctrl+L to smooth it out a bit.
Repeat this process a couple times with more curves. Experiment with colors and opacities.
Now for the finishing touches, we will add the logo.
Put it on its own layer and place that layer right above the background layer. Use Multiply for blend mode. Play with the size and opacity to your liking. I placed mine in the top left corner and turned the opacity to 15% so it is not very noticeable.