Mad circles (also known as interference or moire effect) seem to belong to the first wave of demos effects (even tho not as old as vectorballs or dots) as you can see some in the 1991 Ooh Crickey Wot a Scorcher demo by The Lost Boys. In my humble opinion this is more an effect to be seen as a transition between two screens or used as a demo filler.  Yet if used with style and originality they can still be enjoyable to watch.

Mad circles can be described as two targets (from a darts game) moving around individually and crossing each other. Since they are made of a different color, each time they cross they create a sort of coloured interference (by the way that effect seem to be mostly known as interference by some people).

Maybe not ass kicking but surely nice looking thanks to the picture painted by Exocet. Taken from the 2001 Odd Stuff demo by Sector One and Dune.
The picture helps a lot  taking this simple effect above pure boredom. As it is it looks very stylish. Taken from the Takeover demo by Lamers. (2014)

Sometimes the standard round shape can be replaced by a star or flowerlike pattern. As far as technique is concerned it makes no difference yet it ends up being way more interesting on a design point of view.

Same effect, different shape ! Taken from the very nice Yanartas demo by Checkpoint. (2014)
This time the effect is displayed in fullscreen ! (have a look at the other picture right above and you will see) ! Taken from the 2014 SNDH 4.4 intro by Dead Hackers Society.

These mad circles look better than the usual effect  maybe because of the slight distortion. Anyway it totally fits the perfection of the 2012  Muda demo by Live!. The show is fully enjoyable from start to end be it technically or in style !

The mad circles seen above and taken from the Second Reality 2013 demo by Checkpoint (being a remake from a famous PC demo) are furiously shaken by an additional distortion effect.

Special kudos to Paradox who bring us very special and coloured mad circles in their 2011 Blue Period demo :

Last but not least we turn back to Checkpoint with their 2014 Yanartas demo. This time we are offered quite a nice show of mad circles from their classic shape up to more twisted ones !