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Repeatedly folding a strip of paper in half and unfolding it in straightangles produces a fractal: the dragon curve. Shallit, van der Poorten andothers showed that the sequence of right and left turns relates to a continuedfraction that is also a simple infinite series. We construct a Mahler functionfrom two functions of Dilcher and Stolarsky with similar properties. Itproduces a predictable irregular continued fraction that admits a regularcontinued fraction and a shape resembling the dragon curve. Furthermore, wediscuss numerous variations on this theme.

Fractions, Functions and Folding. A Novel Link between Continued Fractions, Mahler Functions and Paper Folding