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I wish that the Wolfram articles would describe a little more about what their algorithms do, rather than the mechanics of how to use their primitives. The articles remind me some of the era of web engines optimized for a specific task -- there were plenty of MVC frameworks that work really really well for writing a todo list in 25 lines, but doing anything more complicated than a todo list meant dissecting the guts of the framework.

It'd be great to hear how they did an efficient implementation of texture synthesis. But if you want to read at least about the basics, the dissertation they linked [1] gets into the details on page 18, anyway, in section 2.2 (and beyond).

[1] http://www.logarithmic.net/pfh-files/thesis/dissertation.pdf

Re: basics, here is one of the least efficient texture synthesis algorithms, but is detailed, an excellent starting place for beginners, and produces very high quality texture synthesis: http://graphics.cs.cmu.edu/people/efros/research/NPS/alg.htm...

That is from my favorite texture synthesis paper of all (Efros & Leung '99), for these reasons:

- I know Efros, and he's a genius, and also an absolutely adorable human being.

- This paper was inspired by Markov text generators, its the two-dimensional equivalent, e.g., http://en.wikipedia.org/wiki/Mark_V_Shaney. Its very simple, produces great results, - AND - this texture synthesis algorithm will synthesize written text from a picture of written text. Almost none of the faster texture synthesis algorithms do this, and it seems meta; I like to think there is some deep fundamental truth hiding in there somewhere.

(edited for typos and formatting)

Wolfram has a habit of creating blog posts about the test cases for their algorithms.

He also has a habit of not talking about how things work. All the time. Source code, mathematical proofs, citations, all of these things are relatively unimportant in Wolfram's world. He even thinks you should not try to find out how things work:


Particularly in more advanced applications of the Wolfram System, it may sometimes seem worthwhile to try to analyze internal algorithms in order to predict which way of doing a given computation will be the most efficient. And there are indeed occasionally major improvements that you will be able to make in specific computations as a result of such analyses. But most often the analyses will not be worthwhile. For the internals of the Wolfram System are quite complicated, and even given a basic description of the algorithm used for a particular purpose, it is usually extremely difficult to reach a reliable conclusion about how the detailed implementation of this algorithm will actually behave in particular circumstances.

Trust us, we're professionals!

Yeah, I find this article very insulting and condescending. "Don't worry your pretty little head, our ideas are far too complicated for you to understand!"

Its a They, not He. The post isn't written by Wolfram himself :)

The Principle of Computational Equivalence says that Wolfram and his employees are equivalent, right?

How do you know? This article has been up for as long as I've known Wolfram to have a website. I strongly suspect he wrote it himself.

You'd be surprised to know what fraction of the documentation he's actually written himself.

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