Hi Kepa,
Frame 0 doesn’t have to be the same as Frame 250; in order to get the same sequence each time it loops, Frame 1 has to be the same as Frame 1.
The problem is, when the ‘flashing’ is too slow, then the pattern of the rings ‘jumps’ too obviously between Frame 250 and Frame 1. Increasing the speed (the W Values) and/or the Scale of the Texture should make things better.
Alternatively, you could put the Random Value before the Instancing (through Geometry Nodes), as I’ve shown in the other post. Then each Instance would use the same pattern.