The iterative function

1/(z+1)

Starting with 1.5

1.67

1.6

1.625

1.615384

1.619047

1.61764706

1.6181818182

1.617977

1.61805556

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2 Replies to “Golden ratio”

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The iterative function

1/(z+1)

Starting with 1.5

1.67

1.6

1.625

1.615384

1.619047

1.61764706

1.6181818182

1.617977

1.61805556

I think your parentheses are in the wrong place. I think that what you meant was the function

1/z + 1

The function you wrote, when starting with 1.5, gives: 0.4, 0.7142857, 0.5833333, 0.6315789, 0.6129032, 0.62, 0.61728395, etc.

That is, the function you wrote (with the parens) converges to 1/φ and not, as the function you named, to φ.

I think this question is more interesting: what happens if you start with -0.618033989 ?