I find it interesting that the interviewer almost calls out on the disappointing fact that the surface smoothness is essentially just "blobized" interpolation: "It doesn't seem very subtle." It's like when a director has run the film through some colorizing filter to give it a desired tone and you can tell to the point of it becoming distracting.
In case someone is interested in the "eigenanalysis," the recursion formula is:<p><pre><code> [1/2, 1/2, 0 ] [A^n] [A^n+1]
[1/8, 3/4, 1/8] [B^n] = [B^n+1]
[0, 1/2, 1/2] [C^n] [C^n+1]
\_____ _____/
M
</code></pre>
And the question is, given [A^0,B^0,C^0], find [A^∞,B^∞,C^∞], which is equivalent to computing the infinite power of M. Waaaat? Enter the eigendecomposition.<p>The eigenvalues of M are 1/4, 1/2, and 1. If you compute M^∞, the 1/4 and 1/2 "eigenspaces" will disappear, so you're left with the subspace of the eigenvalue 1. <a href="http://bit.ly/eigenex001" rel="nofollow">http://bit.ly/eigenex001</a> M^∞ = Q<i>L^∞</i>Q.inv(), hence the [1,4,1] appears... very cool.<p>Sometimes procrastinating by reading HN actually helps with your work---today I'm working on problem sets for book 2 <a href="http://gum.co/noBSLA" rel="nofollow">http://gum.co/noBSLA</a>