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Topic:collatz
1 project found · topic: collatz
- Collatz Triangles: why does φ appear in the triangles the orbits draw?
Plotting Collatz (3n+1) orbits as coordinate points tiles a wedge with triangles whose side lengths encode the golden ratio: (D₂+D₃)/D₁ → φ. Strong numerical evidence, no proof yet — and a possible link to the golden-mean shift of the 3x+1 itineraries.
Prove the Collatz-triangle side ratios tend to √5, √5/2, ½ (so (D₂+D₃)/D₁ → φ), and determine whether this geometric golden ratio is the same phenomenon as the golden-mean shift of the 3x+1 itineraries.
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