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Collatz's Ant
This is a brief continuation of a previous post (Repo), which introduced such visualization for collatz sequences based on Langton’s Ant. Collatz’s Ant is based on the collatz function:\[f(n) = \begin{cases} n/2 & \text{if} \quad n \equiv 0 \quad (\text{mod}\, 2) \\ 3n + 1 & \text{if} \quad n \equiv 1 \quad (\text{mod}\, 2) \\ \end{cases}\] and additionally, if $n \equiv 0 \, (\text{mod}\, 2)$ the ant turns 90º clockwise, else the ant turns 90º counter-clockwise.
This is a brief continuation of a previous post( Repo), which introduced such visualization for collatz sequences based on Langton’s Ant. And although this representation is interesting, the flipping of state can eventually lead to ambiguous scenarios where trajectories seem similar to each other through omission. Given that, the following picture corresponds to the ant’s landscape (final snapshot) without state flipping for the same trajectories, along with respective stopping times.
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