Random Walk Hexogonal lattice

[SalamuB]

Hello,

I have written a code for 2 dimensional square lattice Random Walk and calculated its Mean square Displacement. Now, I have a problem of changing it to hexagonal lattice. In the code, I have 4 possible directions, Now I need to have 6 possible directions of moving particle. Does anyone know how should I change the directions? Here is the code:

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include <float.h>
#include <limits.h>
#include <sys/types.h>
#include <sys/times.h>

#define TIME 1000 /* number of time steps */
#define FLAG 100
#define NP 10000  /* number of "particles" */


double rndm(void){
  return(double)rand()/RAND_MAX;
}



int main()
{
  FILE *myfilename;
  int i,j,t;
  int pos[NP+5][2];
  double msd,xhelp;
  int xdummy,xint;

  /* Set up random number generator */
  srand(time(NULL));

  /* Set up output file */
  if((myfilename=fopen("RandomWalkHexo.txt","w"))==NULL){
    printf("It didn't succeed to open 'RandomWalkHexo.txt' file.\n");
    printf("Exiting...\n");
    exit(0);
  }
  fprintf(myfilename,"# Time|    MSD    \n");
  fprintf(myfilename,"#=================\n");
  
  /* Set initial position to zero */
  for(i=0;i<NP;i++){
    for(j=0;j<2;j++){
      pos[i][j]=0;
    }
  }
  
  /* Start of main loop */
  xdummy=0;
  for(t=1;t<=TIME;t++){
    xdummy++;
    for(i=0;i<NP;i++){
      /* Move particle to the right or to the left */
      xhelp=rndm();
      if(xhelp<0.25){ 
        pos[i][0]--;
      }
      else{ 
        if(xhelp<0.50){
          pos[i][1]--;
	}
	else{
	  if(xhelp<0.75){
	    pos[i][0]++;
	  }
	  else{
	    pos[i][1]++;
	  }
	}
      }
      /*fprintf(myfilename,"pos[%d][0]= %d, pos[%d][1]= %d\n",i,pos[i][0],i,pos[i][1]);*/
    }
    if(xdummy==FLAG){
      /* Calculate mean square displacement (MSD) */
      msd=0.0;
      for(i=0;i<NP;i++){
        msd=msd+(pos[i][0]*pos[i][0])+(pos[i][1]*pos[i][1]);
        /*fprintf(myfilename,"msd= %lf\n",msd);*/
      }
      msd=msd/((double)(NP));
      /*fprintf(myfilename,"t= %5d, MSD= %10.5lf\n",t,msd);*/
      fprintf(myfilename," %5d  %10.5lf\n",t,msd);
      xdummy=0;
    }
  }

  fclose(myfilename);

}

[nonoob]

Think of a hexagonal matrix as a regular matrix, except every odd row is shifted:

. . . . .
 . . . . .
. . . . .
 . . . . .

So the six directions you can travel depend on whether you're on an odd row or even row. You'll have to work the X and Y coordinate displacements for each direction.

[SalamuB]

nonnob, thank you for your respond. It helped me. Should I illustrate X, Y coordinate displacement in degrees? I am struggling of illustrating the coordinates in the code itself.

[nonoob]

No. You just need to define the 6 directions. How about a clockwise system.
Row [0], [2], [4]...
direction 0 - row--
direction 1 - col++
direction 2 - row++
direction 3 - row++, col--
direction 4 - col--
direction 5 - row--, col--

Row [1], [3], [5]...
direction 0 - row--, col++
direction 1 - col++
direction 2 - row++, col++
direction 3 - row++
direction 4 - col--
direction 5 - row--