\datethis @* One-dimensional particle physics. This program is a quick-and-dirty implementation of the random process analyzed by Hermann Rost in 1981 (see exercise 5.1.4--40). Start with infinitely many 1s followed by infinitely many 0s; then randomly interchange adjacent elements that are out of order. @c #include #include #include "gb_flip.h" char *bit; int *list; int seed; /* random number seed */ int n; /* this many interchanges */ main(argc,argv) int argc; char *argv[]; { register int i,j,k,l,t,u,r; @; @; for (r=0;r; @; } @ @= if (argc!=3 || sscanf(argv[1],"%d",&n)!=1 || sscanf(argv[2],"%d",&seed)!=1) { fprintf(stderr,"Usage: %s n seed >! output.ps\n",argv[0]); exit(-1); } @ We maintain the following invariants: |bit[k]=1| for |k<=l|; |bit[k]=0| for |k=u|; the indices |i| where |bit[i]>bit[i+1]| are |list[j]| for $0\le j= gb_init_rand(seed); bit=(char*)malloc(2*n+2); list=(int*)malloc(4*n+4); for (k=0;k<=n;k++) bit[k]=1; for (;k<=n+n+1;k++) bit[k]=0; l=u=n; list[0]=n; t=1; @ @= { j=gb_unif_rand(t); i=list[j]; t--; list[j]=list[t]; bit[i]=0;@+bit[i+1]=1; if (i==l) l--; if (i==u) u++; if (bit[i-1]) list[t++]=i-1; if (!bit[i+2]) list[t++]=i+1; } @ @= @; @; @; @; @ @= printf("%%!PS\n"); printf("%%%%BoundingBox: -1 -1 361 361\n"); printf("%%%%Creator: %s %s %s\n",argv[0],argv[1],argv[2]); printf("/d {0 s neg rlineto} bind def\n"); /* move down */ printf("/r {s 0 rlineto} bind def\n"); /* move right */ @ @= printf("showpage\n"); @ The empirical curve is scaled so that$\sqrt{6n}$units is 5 inches. @= printf("/s %g def\n",360.0/sqrt(6.0*n)); printf("newpath %d %d s mul moveto\n",0,n-l); for (k=l+1;k<=u;k++) { if (bit[k]) printf(" d");@+else printf(" r"); if ((k-l)%40==0) printf("\n"); } printf("\n0 0 lineto closepath\n"); printf("1 setlinewidth stroke\n"); @ The theoretical curve$\sqrt{\mathstrut x}+\sqrt{\mathstrut y}=1$is scaled so that 1 unit is 5 inches. We use the fact that this curve is {\it exactly\/} drawn by PostScript's Bezier curve routines, from the control points$(0,1)$,$(0,1/3)$,$(1/3,0)$,$(1,0)\$. @= printf("newpath 0 360 moveto 0 120 120 0 360 0 curveto\n"); printf(" 0 0 lineto closepath\n"); printf(".3 setlinewidth stroke\n"); @* Index.