Figure 3 - uploaded by Alexander Yurkin
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1D linear random walk along straight horizontal lines (Pascal's triangle). First three iterations. The envelope lines are shown as dashed straight oblique lines . -The units of 1-fraction, -the units of 2-fraction. The sequence of numbers in lines for the 1D case in this example is denoted by . The step size of the random walk is denoted by . The numbers characterizing the triangle are denoted by . (1)
Source publication
A general approach for the recurrent description of 1D, 2D and 3D linear and nonlinear random walks is determined and the concept of a random walk step is introduced. It is shown that the form of random walks and the internal structure of 1D, 2D and 3D linear and nonlinear figures (including empty units) constructed as a result of random walks depe...
Contexts in source publication
Context 1
... this work in contrast to work (Yurkin, 2019 (4)) we consider only one, the first fraction (1-fraction) of a random walk, the second fraction (2-fraction) in this work we consider zero ("0-units") to simplify the presentation but show in figures as squares without numbers . Figure 3 shows a 1D linear random walk along straight lines arranged horizontally (left-right random walk). Such a random walk is given in the book ( Kolmogorov et al., 1995). ...
Context 2
... initial conditions are shown in Figure 3. They provide the appearance of a group of numbers shown in after performing recurrent calculations. ...
Context 3
... provide the appearance of a group of numbers shown in after performing recurrent calculations. The arithmetic triangle shown in Figure 3 contains the unit of 1-fraction and only regular spaces (gaps) which are units of 2-fraction, so we assume that it is completely filled. Regular gaps can be filled by the 2-fraction of a random walk as shown in Yurkin (2019 (4)). ...
Context 4
... most interesting in our opinion are the nonlinear cases shown in Figure 6 (a, b); their envelope curves are parabolas taken with the opposite sign relative to each other. Straight line envelopes are shown in Figure 3. ...
