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As we know, the von Koch curve, Levy C curve and dragon curve are all built by replacing one line with two in a V shape:


I realised the other day that there are three other variants of this construction that I didn't know about, have you seen them before? they look like this, for bend angle 30,60,90:

type 1:




type 2:




type 3:




The last one is interesting because, like the Koch curve, it curls up into a solid area without every overlapping.
http://tglad.blogspot.com.au/2017/04/new-basic-fractal-curves.html