Here are two chordal fragments that can be moved through the symmetrical diminished scale for some very tasty results!
In a E half whole diminished scale, starting with the chordal fragment F G D and than moving this chordal fragment through the E diminished scale, over an E7 chord for example.
FGD EFC# DEB C#DA# BC#G# A#BG G#A#F GG#E
This fragment can be altered from F G D to F G E and than moved through the diminished scale.
FGE EFD DEC# C#DB BC#A# A#BG# G#A#G GG#F
Another thing to look at with the diminished scale is moving certain intervals through it
For example moving sevenths through the diminished scale. This example will use the E half whole diminished scale over E7
FE ED DC# C#B BA# A#G# G#G GF
These same notes can be intverted to half steps
This idea can also work with alternating major thirds and perfect fourths, perfect fifths and minor sixths
Minor thirds, tri-tones and major sixths can be used to harmonize the diminished scale and be both diatonic and parallel, any interval that is a multiple of a minor third can function in this way