Mathematica and Self-Reference

Some self-documenting sentences (and such) generated with Mathematica:

While searching for the last sentence, I was hoping there would be some striking correlations among the simultaneous counts of letters—say, t’s, e’s, and n’s—as the iteration went along (something like the Lozi attractor, perhaps), but it doesn’t look like it.

For what it’s worth:

Plot of t vs. e vs. n:

(t, e, n)

Plots of e-vs.-t, e-vs.-n, and t-vs.-n:

(e, t) (e, n) (t, n)

From one successful search that took 807 iterations:

e t n
Final 39 25 22
Mean 39.9722.5623.76
Variance 8.17 3.59 4.01

See, of course, Hofstadter, D. R., Metamagical Themas; Chapter 2, “Self-Referential Sentences: A Follow-Up”, and Chapter 16, “Mathematical Chaos and Strange Attractors”; Basic Books, New York, 1985.

© 1998 Robert Dickau.

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