What I call the wreath attrac­tor isn’t a chaotic or strange attrac­tor in the math­e­mat­i­cal sense. But I started using the name and it kind of stuck.

I guess the most we can say is that it’s a transform:

In my imple­men­ta­tion p0 to p4 are nor­mal real para­me­ters with typ­i­cal ranges from –1 to +1 for p1 to p3. p0 and p4 are about 10 times larger. p5 is a spe­cial case and can take only dis­crete val­ues: 0.5, 1, 1.5, 2, 2.5,…

This sys­tem of equa­tions lends itself well to exper­i­men­ta­tion. For exam­ple, lim­it­ing the source, the pos­si­ble start­ing posi­tions of the trac­ing par­ti­cles, has a pro­found impact on the final look. A strik­ing exam­ple is used in the animation. 10 con­cen­tric cir­cles serve as the source and the result­ing image is what you get when the cir­cles are iter­a­tively trans­formed a hun­dred times.

Dur­ing the ani­ma­tion, the para­me­ters p1 to p3 are slightly tweaked from frame to frame. The con­vo­luted geom­e­try is quite sen­si­tive so the changes are smaller than 0.001.  Each frame con­sists of 5 mil­lion par­ti­cle iter­a­tions, tak­ing a few sec­onds to ren­der. The retro flick­er­ing effect is a result of the sta­tis­ti­cal nature of the process,  giv­ing a slightly dif­fer­ent expo­sure each frame.