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UnboundedFigures
UnboundedFigures
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  • avatar
    Tyler Samuels
    @tsamuels
    Aug 22

    The same golden ratio keeps coming back at each period doubling

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  • avatar
    Tyler Samuels
    @tsamuels
    Aug 22

    The one place the golden map gives you φ exactly is its fixed point

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  • avatar
    Tyler Samuels
    @tsamuels
    Aug 22

    In the golden map, the 2-cycle line length runs straight to 1 + φ

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  • avatar
    Tyler Samuels
    @tsamuels
    Aug 22

    Each of those numbers spawns a whole ladder by multiplying by 2

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  • avatar
    Tyler Samuels
    @tsamuels
    Aug 22

    A family of Collatz starting numbers you can fully solve: 1, 5, 21, 85, 341

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  • avatar
    Tyler Samuels
    @tsamuels
    Jul 25

    Plotting Collatz orbits as points draws triangles whose sides give φ

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  • avatar
    Tyler Samuels
    @tsamuels
    Jul 25

    A bifurcation map that keeps drawing the golden ratio

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  • Tyler Samuels · Jul 25

  • Tyler Samuels · Jul 25

Active Projects

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  • The Golden Map: why does φ keep appearing in its periodic points?

    Tyler Samuels · 1 figure

  • Collatz Triangles: why does φ appear in the triangles the orbits draw?

    Tyler Samuels · 1 figure

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  • avatar

    Tyler Samuels

    @tsamuels

UnboundedFigures
UnboundedFigures

A place where math gets done.

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