Techniques: Zoom Bursts
Zoom bursts are where you change the zoom level during the exposure. There are several different looks you can achieve, either by simply zooming in/out and by choosing the rate by which you zoom in i.e. quickly, slowly, smoothly or in a staggered manner. The rate of zooming will affect the strength of the light trails. A lot of these effects work best with a tripod but in some instances you can do it handheld. The following images are slightly different because they don't really make use of light painting. Instead you use the light available in the scene to create the images.
What you can do is create a general image by leaving your camera steady for the majority of your exposure time and then only shifting it at the last few seconds of the exposure. You can shift it by changing the zoom or by moving the camera around. As the lights are so bright, they will imprint on the image instantaneously as opposed to the darker parts of the image which would be to dark to imprint in such a short period of time.

18-135mm 30s F11 ISO 100 - Yarra River, Melbourne Australia
The shot above is a cityscape shot I took in Melbourne. I took this shot using a 30 second exposure and for the first 28 seconds I left the zoom steady at 18mm. Then during the last two seconds I smoothly shifted them zoom all the way from 18mm to 135mm to help give this effect. This way I could create the light trails against the main image.
If you don't leave the camera with the same view for the major part of the exposure, that is you just slowly zoom the whole time, you will basically ended up with a complete blurred image. This technique doesn't always work because it does rely on some interesting arrangement of lights to be somewhere in the centre of the image. The rate of zoom will affect the brightness of the trails. If you are bumpy in your zooming, you will leave trails that are inconsistent. If you stop somewhere along the way, you may create a ghost image. Again all these give different effects and so it's up to you to experiment to determine what looks best in the situation you're in.
Below are some more example images with an explanation of how to get these effects

18-50 1s F3.2 ISO 200 - Martin Place, Sydney, Australia
For this photo, I combined a zoom burst with a front curtain sync. The flash froze his face in place and then I zoomed in quickly. I originally had his face in the centre so that the lines would converge on his face. I then cropped it to get this composition.

18-35mm 10s F10 ISO 100 - Darling Harbour, Sydney, Australia
For this photo, I kept it zoomed out for the first 9 seconds and then zoomed in during the last second.

18-35mm 20s F5.0 ISO 100 - Blue's Point Reserve, Sydney, Australia

18-35mm 20s F5.0 ISO 100 - Blue's Point Reserve, Sydney, Australia
This shot and the one above is had the same setting, however, the difference is that in the first shot, I zoomed in quite quickly whereas as in the second I zoomed in more slowly which is why the trails are more pronounced in the second photo.

18-135mm 36s F7.1 ISO 100 - Milson's Point, Sydney, Australia
In this shot, I staggered the zoom at the end of the shot rather than zooming in smoothly. THis is why you have some ghosting of the bridge in the photograph.

18-35mm 5s F5.6 ISO 100 - Spanish Steps, Rome, Italy
This shot used two different zoom levels, rather than slowly zooming in, I quickly changed between the two zoom levels halfway through the exposure. This is the reason for the ghosting effect on the image.

18-135mm 1S F6.3 ISO 100 - Milson's Point, Sydney, Australia
This shot uses the same concept as the previous ones except instead of zooming in, I picked up the camera and moved it around.
So there you go, there's another idea for you to try out. See if you can combine it with other techniques such as night portraiture to see what sort of things you can come up with.