Geodesic
The Hausdorff dimension of the harmonic measure on de~Rham's curve
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 206-223

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In the paper [3] J. de Rham studied the curve, which can be constructed by “trisecting” the square. Another way to define the curve is to consider the iterated function system, based on two affine transformations. The aim of the present paper is to evaluate the hausdorff dimension of the harmonic measure on the curve. 
@article{ZNSL_2001_283_a13,
     author = {P. P. Nikitin},
     title = {The {Hausdorff} dimension of the harmonic measure on {de~Rham's} curve},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {206--223},
     publisher = {mathdoc},
     volume = {283},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a13/}
}
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P. P. Nikitin. The Hausdorff dimension of the harmonic measure on de~Rham's curve. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 206-223. http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a13/