20,000 1-D random walks are taken, the summation of Gaussian distributed steps with mean of 0 and variance = 1 or uniformly distributed steps from -1 to 1. The positions at a specific step number are

Description

 1 DIMENSIONAL DIFFUSION, RANDOM DIRECTION, RANDOM STEP SIZE
   
   N walks (nwalks) are taken consisting of N steps (nsteps). Each 
   walk starts at x=0. The steps are either left or right depending 
   on a uniform random number(0 to 1) being greater than 1/2; the 
   step lengths are taken from a uniform random distribution from
   0 to 1. The final positions are gridded into bins of width xL.delta. 
   The distribution and the cumulative distributions are plotted along
   the expected Gaussian distribution and the expected cumulative
   distribution. The Gaussian distribution is given by

      Gaussian distribution = (A/(sigma*sqrt(2*PI))*exp(-(xL-xmean)^2/(2*sigma^2)));

   where A= xL.delta, tmean=0, and sigma = sqrt(ntime/3) for steps drawn from
   the uniform distribution from -1 to 1, or sigma = sqrt(ntime) for
   steps drawn from the Gaussian distribution with mean = 0 and variance = 1.

A Gaussian model fitting the end positions of a 1-D Random Walk.

Ten 1D random walks.

Equations

None.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.