A few more with that freebee Image Analyzer I referred to (quite the swiss army knife, really!), using the sample image, enlarged 800%

Wiener 4:
wiener 4.png

Two of the fractals (no idea what the parameters do just playing). I got the best results by going x2, x2, x2 rather than straight (the image names include the parameters):
resize_Temp x2 region=7 regul=0 x2 region=7 regul=0 x2 region=7 regul=0.png
resize_Temp x2 region=9 regul=0 x2 region=9 regul=0 x2 region=9 regul=0.png

And two more from Gimp - progressive resize, 800% in 20 steps:
gimp_resize_steps.png

and a gimp plugin "smart enlarge" using resyntherizer(?) I enlarged 2x 2x 2x. The first was OK, but after that it certainly added detail, but bolloxed up the image:
gimp_resynth_1.png

-Rob A>