Illustrating Irrationality

Inspired by the video by Numberphile, The Golden Ratio (why it is so irrational), which analyzes the relationship between numbers' continued fraction representaions and their 'degree of irrationality'. Here, I have implemented an interactive web-based version of the illustration.

To render different spirals, specify numeric values or (JavaScript) expressions in the input field. (Hint - Try clicking on the Spiral canvas and using up/down arrow keys to modify the spiral ratio.)