2-Mirror System
2 mirrors are arranged such that they form a V shape. The third side of the triangle should be a blackened, non-reflective surface. The angle of the V determines the number of reflections contributing to the intricacy of the pattern.
Considering the center O, mirror OA and OB, the object will be reflected off OA and OB to form virtual images in OAD and OBC respectively. The virtual images of OAD and OBC will reflect off OD and OC respectively and form more virtual images, ODE and OCF. This continues way round the circle until a kaleidoscopic image is formed. The order of reflections is as above.

An inaccurate overlap would inherently destroy the closure of the symmetric pattern. Therefore a basic rule of thumb in a 2-mirror scope is that the angle of the mirrors must evenly divide the 360 of a circle.

So, starting with a 90 angle, the image produced would have 4 fold symmetry (FIG 2).
45    -   8 fold symmetry   - 4 point star
36    -  10 fold symmetry  - 5 point star
30    -  12 fold symmetry  - 6 point star
22.5 -  16 fold symmetry  - 8 point star
15    -  24 fold symmetry  - 12 point star
10    -  36 fold symmetry  - 18 point star
1      - 360 fold symmetry - 180 point star