Jonathan. Frech’s WebBlog

𝜑 generator (#15)

Jonathan Frech, 9 April 2015

This program generates 𝜑, also called the golden ratio. It creates the fibonacci sequence $\big\{1,1,2,3,5,8,13,\dots\big\}$ $\big\{1,1,2,3,5,8,13,\dots\big\}$ and divides the newly generated number by the last one. In theory this program would generate exactly⁠¹ 𝜑.

Fibonacci sequence

$\text{Start: }x_1=1\text{ and }x_2=1$ $\text{Start: }x_1=1\text{ and }x_2=1$
$\text{Generation: }x_n=x_{n-1}+x_{n-2}$ $\text{Generation: }x_n=x_{n-1}+x_{n-2}$
$8+13=\dots$ $8+13=\dots$

The golden ratio (𝜑)

$\phi\text{ is the ratio between }x_n\text{ and }x_{n-1}\text{.}$ $\phi\text{ is the ratio between }x_n\text{ and }x_{n-1}\text{.}$
$\phi=\frac{x_n}{x_{n-1}}$ $\phi=\frac{x_n}{x_{n-1}}$

Source code: phi-generator.py

[1]	[2020-07-08] Assuming infinite time and memory it would compute 𝜑 in its limit.