The image kind of looks like a closed eyelid or a sideways cat's eye.

This fractal was synthesized by repeatedly zooming into specific areas in order to create a line of repeated features. For a general method that forms a line from a Mandelbrot set fractal with a minibrot see this page.

The parameter file used to make the image is below:

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 }