Hi Dr. Wolfram,
I hate to be one of those guys who says "Nice paper, now please read mine," but in this case, since I titled my paper in homage to your book "A New Kind of Science," I couldn't resist piling on with exactly such a request.
Your paper seems to be a great distillation of many of the themes emerging from different contestant's submissions. Plus, it has the benefit of being written conversationally and in a natural, engaging tone. Bravo.
The very earliest spark of my paper was, right after I finished "A New Kind of Science," I read Seth Lloyd's book "Programming the Universe," and thought to myself, "This is the first time I've purchased a book with the word 'programming' in the title that hasn't contained a single line of source code." To co-opt the terminology of pure mathematics, the digital physics community seems to have contented itself with producing existence proofs, but not constructions. That community seems to agree that "Yup, the entire universe could indeed be software," but nobody seems to have taken the next logical step, to say "OK, what might that software look like? How might its source code be constructed?" My paper offers up a starting point for exploring such possible constructions. That starting point is, as is yours, fundamentally graph-theoretic in structure. More specifically, it is a fractal that operates within graph-theoretic space.
Traditional fractals like the Mandelbrot set, Menger sponge (indeed anything listed at http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_d
imension) consume a subset of traditional n-dimensional space; part of the reason a Sierpinski triangle's Hausdorff dimension is less than 2 is that a complete representation of it can fit inside a 2-dimensional plane. The same reasoning ensures that the Menger sponge's Hausdorff dimension is less than 3. No fractal at the wikipedia page has a Hausdorff dimension greater than 3.
I wonder if part of the reason this is the case is that traditional fractals, because they work by "claiming" points within a larger predefined space, can only _consume_ space. The fractal I propose in my paper (the "Object" class) simultaneously consumes _and_generates_ space (by "claiming" points/nodes and then also having a mechanism for creating new points/nodes). This means, if we were to find a suitable generalization of Hausdorff dimension that can take graph-theoretic fractals into account, then the "Object" class's Hausdorff dimension could be something greater than 3. It could even be, for instance, pi.
Anyhoo, the other day I was lamenting to Ray Munroe Jr that "I wish someone who had as much history as I do with computation, and also as much history as you do with physics, would read the paper and comment on it." Seems to me you're just the right man for the job -- or, at worst, overqualified.