To some of you I recently blathered that the only known rotationally symmetric (modulo slight smushing) "recursive" trinskys were of orders 3 ,4, 5, and 6, completely forgetting the 8 and 12 found by my coauthors. But I don't think we had a 10 until gosper.org/TrinskyXYPlot[599,599,3÷2-√5÷2,1÷2,0,0,1,1,999999][[8,3]].png , which has an infinite hierarchy of nested "star loops". gosper.org/monstar.png . Empirically, they can be started at x = y = 4 + 2 GoldenRatio^(-5 - 2 n)/√5 + 2 GoldenRatio^(5 + 2 n))/√5, with period 140/3 (5 4^n - 2). --rwg PS here's an 8: gosper.org/octoplasm.png and a 12: gosper.org/dodecadence.png .