Tyler Samuels
@tsamuels
Founder of UnboundedFigures.
Open to collaborate
Joined
10/4/2025
Submissions
7
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0
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Topics
#golden-ratio#dynamical-systems#bifurcation#periodic-points#golden-map#collatz#3n+1#number-theory
Projects
Browse all- The Golden Map: why does φ keep appearing in its periodic points?Activedynamical-systemsbifurcationgolden-ratiorenormalizationopen-problem
1 figure · active yesterday
- Collatz Triangles: why does φ appear in the triangles the orbits draw?Activecollatz3n+1golden-rationumber-theoryopen-problem
1 figure · active 1mo ago
Public Work
Contributions by @tsamuels
Tyler Samuels
@tsamuels
The same golden ratio keeps coming back at each period doubling
8/22/2026, 2:19:43 PM • Dynamical Systems
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Tyler Samuels
@tsamuels
The one place the golden map gives you φ exactly is its fixed point
8/22/2026, 2:19:43 PM • Dynamical Systems
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Tyler Samuels
@tsamuels
In the golden map, the 2-cycle line length runs straight to 1 + φ
8/22/2026, 2:19:43 PM • Dynamical Systems
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Tyler Samuels
@tsamuels
Each of those numbers spawns a whole ladder by multiplying by 2
8/22/2026, 2:08:30 PM • Number Theory
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Tyler Samuels
@tsamuels
A family of Collatz starting numbers you can fully solve: 1, 5, 21, 85, 341
8/22/2026, 2:08:30 PM • Number Theory
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Tyler Samuels
@tsamuels
Plotting Collatz orbits as points draws triangles whose sides give φ
7/25/2026, 4:26:36 PM • Number Theory
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Tyler Samuels
@tsamuels
A bifurcation map that keeps drawing the golden ratio
7/25/2026, 5:54:05 AM • Dynamical Systems
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