Random walk diffusion in two dimensions with choice of fixed step size, random step size, random direction and step size.

Description

	This model simulates the simplest of the diffusion problems, that of one particle 
 moving in two dimensions with equivalent directional diffusivities. This simulation 
 utilizes a random number generator to calculate the x and y movement of any 
 given step in the random walk process. In the visualization above a set of nstep 
 moves are made which are shown in green. At the end of every nstep moves, an endpoint is 
 reached and a mark is made which is indicated by the red star. After nmark sets of 
 nstep moves the simulation ends.

	For each step, two random numbers are chosen from a uniform distribution between
0 and 1. If  the user has chosen fixed steps, the x and y steps are plus or minus 1
dependent on whether the random numbers are greater than a half. If the user has chosen
variable steps, the random numbers are scaled to be between -1 and +1. If the user has chosen
angle and step random, the step is the first random number and the direction multiplies
the second random number by 2*PI.

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.