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Numerically, the gap between orbit points shrinks by about 1/φ each step.
Nice, that gives us the contraction bound we need for the paper.
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See all →The same golden ratio keeps coming back at each period doubling
Tyler Samuels · Dynamical Systems · 0 upvotes
A family of Collatz starting numbers you can fully solve: 1, 5, 21, 85, 341
Tyler Samuels · Number Theory · 0 upvotes
A bifurcation map that keeps drawing the golden ratio
Tyler Samuels · Dynamical Systems · 0 upvotes
Each of those numbers spawns a whole ladder by multiplying by 2
Tyler Samuels · Number Theory · 0 upvotes
The one place the golden map gives you φ exactly is its fixed point
Tyler Samuels · Dynamical Systems · 0 upvotes