Bill Gosper, Continued Fractions and The Dragon Curve

See Daniel Tubbenhauer on p-adic Arithmetic and Norman Wildberger's Five Fingered Gauntlet For Pure Mathematicians.


Subscribe to G4G Celebration.

See GXWeb Continued Fraction Arithmetic which is an online tool for computing with continued fraction expansions.


Here's a description of the Dragon Curve in terms of the parity of folds you get when you repeatedly fold a piece of paper in half in the same direction, then open it out just a bit and look down on the edges of the paper sheet. Look at the 90 degree turns as your eye follows along the edge. As the number of folds increases, you generate a sequence like this: R, RRL, RRLRRLL, RRLLLRRLLLRL, ... Now the description in the video might make a bit more sense:

Take a piece of paper and fold it in half. Fold a few more times in the same direction, then open out your page. You will see a series of bends, in what at first might seem to be an irregular sequence, but forming what is known as the PaperFold Sequence. If each bend is arranged at 90 degrees, then we form the Dragon Curve Fractal - a beautiful, space-filling curve whose edges never overlap (although some of the vertices do)!

For more on recursive symbolic dynamics and languages to describe processes: for example my favourite one: "do nothing or split", see Numberphile - Sophie Maclean on the Catalan Numbers.


Here's the lecture:

This guy is a genius! See https://compasstech.com.au/ for more.


See this post I made in the De Volada cafe in Tecate, inspired by my friend Livier: On How Language Works With Perception To Construct The World We Live In. Livier wants to go to France too. See also Chiara Christian And Human Design.

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