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Collatz's Ant and Σ(n)
Relevant preceding posts here and here. Consider the corresponding ant’s landscape development for $n = 500$: with the last frame being: Let’s also consider a score function $\Sigma(n)$ which returns the number of 1’s (or marked states) left by the ant on the corresponding landscape (regarding the last frame).
Let’s also consider a score function $\Sigma(n)$ which returns the number of 1’s (or marked states) left by the ant on the corresponding landscape (regarding the last frame). We might also want to normalize this by the corresponding stopping time $\tau_{n}$ characteristic of the collatz function dynamics for a given $n$. Additionally, let’s also consider some metrics relative to the ant’s (euclidean) distance to the origin.
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