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There exist many techniques to create walk cycles. Traditionally, walk cycles are hand-drawn, but over time with the introduction of new technologies for new mediums, walk cycles can be made in pixel art, 2D computer graphics, 3D computer graphics, stop motion, and cut-out animation, or using techniques like rotoscoping.
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line Z {\displaystyle \mathbb {Z} } which starts at 0, and at each step moves ...
The term cycle may also refer to an element of the cycle space of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the binary cycle space (usually called simply the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field.
Original - Two dimensional random walk for one particle on a 400 by 400 lattice. One million steps shown at 1500 steps per second: at each step, the particle randomly moves to any position in its Moore neighbourhood. The lattice has toroidal boundary conditions (i.e. going off one edge reappears on the opposite edge).
2D_Random_Walk_400x400.ogv (Ogg Theora video file, length 11 min 7 s, 400 × 400 pixels, 218 kbps, file size: 17.34 MB) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
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An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once