Title: Some Koch-like curves Post by: Tglad on November 04, 2016, 04:06:14 AM The 'volcanic surface' fractal http://glslsandbox.com/e#4851.17 (http://glslsandbox.com/e#4851.17) has an equivalent 2D curve, it looks like this for increasing bend angle: (https://4.bp.blogspot.com/-cERz19OW7a0/WBhjvx1rjLI/AAAAAAAAA3g/4jzms9eRyhUGubY9Fv35eTqrtCXTY6mDwCLcB/s320/tree180pt125.png) (https://4.bp.blogspot.com/-yF1XMKzjVe4/WBhj1Lf8YOI/AAAAAAAAA3k/EeRZR43kTYQz3WsKnXunljqkEoBSQDMaACLcB/s320/tree180pt25.png) (https://4.bp.blogspot.com/-zDbauj7paJM/WBhj5EFo7MI/AAAAAAAAA3o/hyUpxHS7FFUsJQeVznU5nXroaP0lHDzsgCLcB/s320/tree180pt29.png) Similar to the Koch curve that places each line with 2 lines, this replaces each line with 3, two of which are in an upside-down V shape. If the third line is flipped you get this nice symmetric looking curve: (https://2.bp.blogspot.com/-vOpI75_4oKs/WBhkfxOu6dI/AAAAAAAAA3w/l322fsi5ceE8eilCOKtp2oGZan7C_BcxgCLcB/s320/treeReverseypt125.png) which can go all the way to 60 degrees bend angle before it self-contacts. (https://1.bp.blogspot.com/-1YHx5wxjRYo/WBhkj907PGI/AAAAAAAAA34/b9o_iAm8Oo4E_1Sa2s-eDCB_fmA7QwdWgCLcB/s320/treeReversey60deg.png) and, just like the Koch curve, you can make a snowflake out of it. It does look familiar :-\ |