Geodesic
Spiralling in Plane Random Walk
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 1-6

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A particle is initially at the origin in the (X, Y) plane and each successive step it takes is of unit length and parallel either to the X-axis or to the Y-axis. Its path of n steps is called a spiral if (i) the particle never occupies the same position twice, (ii) any turns the path makes are all counter-clockwise or all clockwise and (iii) for every m > n, the path can be continued to m steps without violating (i) or (ii). 
Wright, E. M. Spiralling in Plane Random Walk. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 1-6. doi: 10.4153/CMB-1965-001-0
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