For the generalized Heighway dragon with parameter theta = pi minus 2 alpha, the graphs of both coordinate functions have box-counting dimension 1 minus log(cos alpha)/log 2, recovering 3/2 for the classical dragon.
Albers, Papierfalten, Doctoral thesis, Bremen Uni- versity, (2006)
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The coordinate functions of the Heighway dragon curve
For the generalized Heighway dragon with parameter theta = pi minus 2 alpha, the graphs of both coordinate functions have box-counting dimension 1 minus log(cos alpha)/log 2, recovering 3/2 for the classical dragon.