You give a nice summary of the book, but it is dangerous to stick to Chaitin's terminology. By his choice of words he inflates the significance of his model, except for the first program, all subsequent 'mutations' produce specific types of programs which are just a self-delimiting header followed by a fraction. The sad part is that he never uses the full power of algorithms at all, and produces a very boring model when it is recast in simpler terms:
Chaitin's model isn't really algorithmic
You give a nice summary of the book, but it is dangerous to stick to Chaitin's terminology. By his choice of words he inflates the significance of his model, except for the first program, all subsequent 'mutations' produce specific types of programs which are just a self-delimiting header followed by a fraction. The sad part is that he never uses the full power of algorithms at all, and produces a very boring model when it is recast in simpler terms:
http://egtheory.wordpress.com/2012/07/08/algorithmic-mutation/
I had very high hopes for this book (much like you) when I saw it in the bookstore. After reading and reflecting, I was extremely disappointed :(.