Three topics:
(1) Genuine Fractal sampling
(2) Gamma correction in saturated images
(3) Upsampling rasterized vector images

(1) Genuine Fractal Sampling
I was interested in the "Fractal" upsampling technique since the literature on image resampling doesn't contain this term --- the closest I could find were statistical techniques for preserving edges and Haar/other wavelet transformations. I found the website for the "Genuine Fractal" (GF) method, and it is interesting to see how it works. I believe, overall, the GF upsampling method is roughly the same as repeated bicubic upsamplings at factors of 2, followed by smoothing, and edge-sharpening to keep the image from blurring. This, effectively, automates the "by-hand" upsampling technique you describe earlier in this tutorial.

I have no clue why they call this "Fractal" sampling, since it does not look like any of the mathematics of fractals. Also, the method is patented, although, the patent is from the early/mid-90s so it is probably close to being expired.

(2) Gamma Correction
I'm not sure the exact colorspace, nor gamma correction method being referred to. However, usually gamma correction occurs in an unclamped colorspace, and samples to a 32-bit floating-point channel. By adding a gamma of .5 for a saturated image, then upsampling, then inverting the gamma to 2, you've applied a isomorphism to all the pixels that maintain their saturation levels (up to round-off error). However, by increasing the gamma, the newly generated pixels (the "dark" muddy pixels between the mauve and green) are gamma'ed out of existence --- they become very light gray. I would propose that a light-gray pixel will be interpreted as a transition zone in the light field your eye picks up, rather than an edge. The dark-gray transition in the light field will be interpreted as an edge. This makes the light-gray transition "look" better without having any discernibly different characteristics, other than being lighter-in-color.

(3) Upsampling Rasterized Vector Images
There are a number of (free) programs for converting from raster images (especially 2-bit raster images) to stroked vector images. I have had success with both POTrace and AutoTrace/Delineate. They can be found here:
http://potrace.sourceforge.net/
and here:
http://delineate.sourceforge.net/
respectively.