Published on: 2025-06-13 13:50:06
Collatz's Ant and similarity of landscapes This is a small development from the previous post, which is mostly focused on trying to understand where the similarities between landscapes come from (and what can be taken as proxies for these). Considering the trajectories respective to the numbers from $n = 10^{20}$ to $n = 10^{20} + 100$, and the corresponding stopping times ($\tau$), maximum euclidean distance hit ($\alpha$) from the origin point $(0, 0)$ where the ant starts, the step at which
Keywords: alpha beta different landscape landscapes
Find related items on AmazonPublished on: 2025-08-14 08:52:08
Collatz's Ant and similarity of collatz sequences 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: and additionally, if $n \equiv 0 \, (\text{mod}\, 2)$ the ant turns 90º clockwise, else the ant turns 90º counter-clockwise. On both accounts, the state of the cell is flipped and the ant moves forward one unit. This is repeated until $n = 1$. An example of suc
Keywords: 10 20 ant landscapes steps
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