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1D walks 1D random walks based on the digits  of  in various bases. If  is even, a step to the right is taken, if  is odd, a step to the left is taken. 1D random walks based on the digits  of  in various bases. If  is even, a step to the right is taken, if  is odd, a step to the left is taken. The left graphic shows the average distance of the walker from the origin, averaged over the first 100 even bases  . The right graphic shows the binned scaled deviation of the individual walks (for a fixed basis  ) from the average. 2D walks 2D random walks based on the digits  of  in various bases  . For each  , a step is taken in direction  . For clarity, the  th step is shown with a  ‐value  . 2D random walks based on the digits  of  in various bases  . For each  , a step is taken in direction  . For clarity, the  th step is shown with a  ‐value  . 2D random walks based on the digits  of  in various bases  . For each  , a step is taken in direction  . 2D random walks based on the digits  of  in various bases  . For each  a step is taken in direction  . Platonic walks 3D random walks based on the digits  of  in various bases  . For each  , a step of size 1 is taken in direction of the  th vertex of a Platonic solid. 2D Levy-type walks 2D Lévy‐type random walks based on the digits  of  in various bases  and numbers of directions  . For each  , a step of length  is taken in direction  . Higher-dimensional walks 2D projections of a  D random walk based on the digits  of  in various bases  . For each  , a step is taken in direction  (the  is on position  ). The resulting visited lattice points are projected into a 2D plane spanned by the vectors  and  .
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