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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:
(https://2.bp.blogspot.com/-_R0F3QqMfPA/WQB-V-KzZ_I/AAAAAAAABO0/tXgzkntk_MouiUc4Ro0K8DkC7_FaSab3QCLcB/s320/curves.png)

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:
(https://2.bp.blogspot.com/-k18j7NEL8a8/WQCFppC2xiI/AAAAAAAABP4/MB5BRrSTgSUsK8Cpl-9Df1ACz50OkHwZgCLcB/s320/new1a30.png)
(https://3.bp.blogspot.com/-2RXFMIcWX2c/WQCAl1nBMCI/AAAAAAAABPQ/Z-cr2Pb2U64lyweIIazj-1gk2-ZDgCPfwCLcB/s320/new1.png)
(https://3.bp.blogspot.com/-OlewLvqkbDU/WQCC2b0rSQI/AAAAAAAABPo/kOPCXP_oWAQjv2N0Dp4dABvjEDEwuc8HQCLcB/s320/new1b.png)

type 2:
(https://3.bp.blogspot.com/-nsyK5zlYja0/WQCF_JCH4DI/AAAAAAAABP8/KxbmNKRPmGI425OIc9a4TBfI4ED3HCUFgCLcB/s320/new2a30.png)
(https://3.bp.blogspot.com/-ERhYvvdGdQY/WQCAl8yBiNI/AAAAAAAABPY/lecwqVsMAvQ7fnbc0osr_x76Hx-lDofrQCLcB/s320/new2.png)
(https://4.bp.blogspot.com/-GHc2UKvb8Ko/WQCB7QvqGtI/AAAAAAAABPg/QWWcrdkf92gicFdstQvB_SsLwUeBAVBEgCLcB/s320/new2b.png)

type 3:
(https://2.bp.blogspot.com/-456CAorwmeQ/WQCGL3PAd0I/AAAAAAAABQA/55jj0ScZ5lE0S9OuZpBl5Y7rE3fwCQR4gCLcB/s320/new3a30.png)
(https://3.bp.blogspot.com/--28zepws698/WQCGq_NR8aI/AAAAAAAABQI/pZ8NEHNNG8UZHfMN_UlPTx-EjFNT7fTDQCLcB/s320/new3.png)
(https://4.bp.blogspot.com/-ZP5xZQLoHL0/WQCC6GxA5SI/AAAAAAAABPs/A4oVyYXHvRcZq09qHVnNIi1F2bHNcmc6QCLcB/s320/new3b.png)

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 (http://tglad.blogspot.com.au/2017/04/new-basic-fractal-curves.html)

  Quick (3d version!!) low res animation of the last one with the 90 degree angle being altered over time?  :D 

  I can't do it on this machine...