That effect is caused by an interference effect.
You just get an image which is made up of concentric circles and overlay it on top of another image which is the same. As they move, it creates this interference effect.
Most of the time on the amiga they would draw these in different bitplanes so that when they overlap the colour can automatically change which gives another type of effect and makes the lines look like they are stretching.
You can generate lots of interesting effects using different patterns and this method
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