Kind of looks like a closed eyelid or a sideways cat's eye.

Here is a link to a web page with an image:

Here is a link to a page with a step by step method for making line fractals:

The parameter file used to make the image:

Shut_Eye { ; Exported from Fracton.

 ; time = 5 min 36 sec at 640 x 480 with no aa

 ; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon

 ; by Mike Frazier, public domain

 reset=2004 type=mandel passes=1 float=y

 center-mag=-0.637200976593501474305583909687372908\

 30227891481784063632604796741094157599156902438932\

 939287497/-0.4949950432196933461151370819730504957\

 83472228433228355943547904232277233494056237054403\

 58652795/5.3333334e+76/1/42/0

 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=0

 proximity=0

 colors=qaHtcGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDT\

 GDQDCNBCK8C413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdS\

 egUikXloZprasvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZ\

 P`XO_UMYRKWPJUMHSJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjA\

 Hm9Jp8Lr7Nu5Px5Nu6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8S\

 H9QJANKBLMCIOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljl\

 olornrulprkmnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQ\

 K8OI5RK7TN9WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_\

 zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAA\

 KADMAGNAIPALQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnC\

 qlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29B145000311632943\

 D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9nH7pH6rH5vH3zH0vH\

 2rG3mE2hD2cB2ZA2U81P71K51F41A30510000330760BA1ED1I\

 G1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq3wu1zz0ww1tt2pp3\

 mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJDBGABD6CA3C80CC4\

 CH8DMCDRGEWKE`OFeSFkWInZH }