If you aren't familiar with the AE, it is a custom Lua command-line interpreter environment with a few of my own extensions built in. I use it for all sorts of things, including the underlying platform for my game, Goblinson Crusoe.
The part that is most relevant to the article is the set of implicit noise functions. AE contains a pretty big set of chainable functions that can be assembled together by writing a Lua table of module descriptors. The article includes the table for a set of descriptors describing a module chain for generating a Minecraftian world, and that table is meant to be parsed by the AE library.
Here is a build of the AE, with included files for experimenting with the method described in the article. The relevant file is called creatorofworlds.lua. Run the Accidental executable, and execute the command "dofile("creatorofworlds.lua")". The result will be a file in the executing directory called "output.obj", which is a Wavefront .OBJ format mesh of the generated chunk (non-optimized, so the mesh file can be dense). The procedure works by mapping a chunk of the implicit module tree to a voxel field, then using the PolyVox library to convert the voxel field to a mesh for export.
If you would like to tinker with things, then edit the descriptors listed in the table minecraftlevel. For a fairly complete (though not exhaustive) description of the various functions you can use, see the file NoiseDoc.txt. The relevant section is under the heading Implicit Functions; these are the functions that operate in pure implicit mathematical space; all functions in this section have variants for 2,3,4 and 6-dimensional noise, and do not operate on explicit buffers of data. The other modules described, Greyscale and RGBA, operate explicitly on chunks of 2D data, typically for my experiments in procedural texture generation.
You build a descriptor table, and feed it to the function NoiseModuleTable() to return a constructed module chain that is ready to go. You can obtain a reference to any of the modules via the member function getFunction(name), and call get(x,y)/get(x,y,z)/get(x,y,z,w)/get(x,y,z,w,u,v) directly on the returned result. (I provide 6D versions to facilitate my method of mapping seamless 2D and 3D noise buffers, as described in my blog entry here).
The binary distribution also includes some code for my later experiments, detailed in this blog post . The code to play with these is found in the file POVRay_MinecraftLevel.lua. This experiment modifies the procedure somewhat, so that rather than outputing Solid/Open, the function chain will output different identifiers for various types of solid rock. The visualizer for this experiment outputs a mesh file meant to be rendered by POVRay; included in the distribution is the file voxelfieldrender.pov, which when executed by POVRay, will render the mesh output by the program.
If you have any questions, let me know.