The Polar grid tool can be used to create many interesting concentric circles designs. Useit with the radial divider set to 0 and concentric divider great than zero (say 10 or 20 etc) and create the art. To create, select the grid tool, double click the icon, set the radial divider to zero, set the divider to 12 or 20 etc to get rings from the grid tool, hold the shift key down, drag outwards to create the artwork, release the mouse, set the fill to no color and the stroke to black etc and the width as required
You can also vary the design with the powerful width feature. You can use the width tool to modify the artwork.
You can also ungroup the art and transform each of the individual items or use the isolation mode (by double clicking on the path until you can access the individual rings) approach to break down the path. Select the artwork, go to the object menu ungroup, object menu ungroup, select individual rings, change the stroke width etc, change the color of the stroke. It is odd but the ungroup needs to be used twice (I am certain there is some reason for this with the paths created with the tool - I am certain that sometimes it ungroups with only one command). Another option is to double click the design and enter the isolation mode where you can move the individual parts of the design, re-color the artwork.
Or use the layers panel (found in the window menu) and then select the individual paths (click the right side marker of the layer entry and set to blue) and then change the paths
The end result is just a set of paths that can be manipulated in multiple ways with effects as well as transformations such as shifting the artwork or scaling or overlapping the design with another set of paths. Select all the rings (or all the rings you want to select), go to the toolbar, select the live paint bucket tool. Click the space between the rings to add the current color, change the color via the fill color etc. Unless you expand the artwork via the object menu and expand command, you won't be able to use the live bucket with the strokes but you can just re-color them individually via the stroke settings for those paths (best to do any re-coloring of the strokes before you use the live paint bucket). You can also save the result to the symbols panel or to the CC libraries for future use
Create a rectangle, place that over one half of the object, go to the object menu and clipping mask and make.
You can also re-color the artwork using the powerful color guide which can be found via the windows menu color guide and then use that to re-color the artwork
Or use another path to create a slice of the artwork by creating a basic triangle and placing that over the design. The easiest way to create the triangle is probably to use the pen tool (click somewhere near the artwork) and then click the middle of the design and then come out back outside of the design and then back to the original point and this will create an arc design instead
Create a set of the designs and then duplicate that by holding down the alt / option key to create another set. You can manipulate the individual paths for those or just shift them slightly to create multiple interesting combinations of the artworks. You can then also use the live paint bucket to fill those with colors as well. You can extend this to multiple combinations with different number of dividers. Go to the toolbar, select the tool, double click the icon, set divider to 5 and radial to 0, set the stroke weight, create a path, set the stroke weight, create another path etc
You can use the paths as is but you can also apply effects to the artwork paths via the effect menu such as punk and bloat, zigzag etc. All kinds of weird and wonderful designs can be created from these paths. Select the tool, double click the icon, set divider to 12 and radial to 0, set the stroke weight, go to the effect menu, distort and transform, use the effect 'punk and bloat', set the slider as required, object menu and expand appearance
You can use the powerful new repeat feature with the artwork. Go to the object menu and repeat and radial with the artwork selected and then change the radius as well as modify the number of instances. Double click the design to access the original object and you can then squeeze, rotate, distort, add effects etc to create all kinds of unique designs in seconds.