Please have a look at the file below:
The yellow cube provides the animation. Which is then given to the Voronoi Fracture’s Fragments (Clones).
In the Inheritance Effector> Effector>… (see image below). You will find the needed setting, that provides the animation to the Fragments based on their ID number. This means that the Step-Gap is the time that each Fragment has compared to the one before or after.
Please let me know if there is any other question about it, as this is undoubtedly a powerful option. It should be in everyone’s “tool-box”.
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