An evening's hack: a tweetable, 139 character dc program to render a
Mandelbrot set.
$ dc -e '?[P5]Pfswshsm9k[q]sQ0sq[0[dlw/4*3-salqlh/3*1.5-sb0ddsxsy[lxd*lyd*+4!>Qlxdd*lyd*-la+sx2ly**lb+sy1+dlm>I]dsIx1-P1+dlw>X]dsXxclq1+dsqlh>Y]dsYx' > mandelbrot.pgm <<<'32 256 384'
Here, 32 is the max iterations (up to 255), 256 is the pixel height, and 384 is the pixel width. The program takes those three parameters from stdin and prints a PGM format grayscale bitmap to stdout.
It might take a while if you use big numbers. 128 1024 1536 took about 15 minutes on my i5 3750K.
A few more characters gets us a color palette. This is compatible with the new 280-character Tweet™ limit, coming in at just over 200 characters.
The palette can be adjusted by tweaking a couple numbers in the code, the meaning of which are left as an exercise for the reader.