## Random walk in the space – fig0010

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 11 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
settings.render=0;

// The available directions of steps
triple[] dirs={X,-X,Y,-Y,Z,-Z};
dirs.cyclic=true;

// Return the nodes of the path
triple[] randWalk(real Srnd(), int n)
{
triple[] randPath;
triple camera=1e10*currentprojection.camera;
triple pos=O, tpos;
int R;
for (int i=0; i < n; ++i) {
R=round(Srnd());
tpos=pos+dirs[R];
randPath.push(tpos);
pos=tpos;
}
return randPath;
}
triple[] randWalk(int Srnd(), int n)
{
real R(){ return Srnd();}
return randWalk(R,n);
}

void drawWalk(triple[] nodes, pen p=white)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(nodes)),abs(maxbound(nodes)));
real[][] depth;
for(int i=0; i < nodes.length-1; ++i) {
real d=abs(camera-0.5*(nodes[i]+nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=nodes[round(depth[0][1])];
triple m=nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(nodes[i]--nodes[i+1],abs(nodes[i]-m)/abs(M-m)*p);
}
}

size(18cm);
currentprojection=orthographic((1,1,1));

drawWalk(randWalk(rand,50000),cyan);
shipout(bbox(3mm,Fill));

```

Étiquettes : , , ,

## Random walk in the space – fig0020

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 12 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
settings.render=0;

// The available directions of steps
triple[] dirs={X,-X,Y,-Y,Z,-Z};
dirs.cyclic=true;

struct walk
{
triple[] nodes;
pen[] p;
}

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, pen[] p={currentpen})
{
p.cyclic=true;
walk ow;
triple pos=O, tpos;
for (int i=0; i < n; ++i) {
int R=round(Srnd());
tpos=pos+dirs[R];
ow.nodes.push(tpos);
ow.p.push(p[R]);
pos=tpos;
}
return ow;
}

walk randWalk(int Srnd(), int n, pen[] p={currentpen})
{
real R(){ return Srnd();}
return randWalk(R,n,p);
}

void drawWalk(walk walk)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
real[][] depth;
for(int i=0; i < walk.nodes.length-1; ++i) {
real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=walk.nodes[round(depth[0][1])];
triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
// dot(walk.nodes[i],walk.p[i]);
draw(walk.nodes[i]--walk.nodes[i+1],abs(walk.nodes[i]-m)/abs(M-m)*(walk.p[i]+walk.p[i+1]));
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(rand,50000,new pen[]{red, blue, green, yellow, purple}));
shipout(bbox(3mm,Fill));

```

Étiquettes : ,

## Random walk in the space – fig0030

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 13 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
import stats;
settings.render=0;

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, B=backward, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
triple[] randWalk(real Srnd(), int n, real angle=90)
{
triple[] randPath;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
string R=dirs[round(Srnd())];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
randPath.push(tpos);
pos=tpos;
nextdir();
}
return randPath;
}

triple[] randWalk(int Srnd(), int n, real angle=90)
{
real R(){ return Srnd();}
return randWalk(R,n,angle);
}

void drawWalk(triple[] nodes, pen p=white)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(nodes)),abs(maxbound(nodes)));
real[][] depth;
for(int i=0; i < nodes.length-1; ++i) {
real d=abs(camera-0.5*(nodes[i]+nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=nodes[round(depth[0][1])];
triple m=nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(nodes[i]--nodes[i+1],abs(nodes[i]-M)/abs(M-m)*p);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(Gaussrand,50000));

```

Étiquettes :

## Random walk in the space – fig0040

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 14 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
import stats;
settings.render=0;

struct walk
{
triple[] nodes;
pen[] p;
}

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, B=backward, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, real angle=90, pen[] p={currentpen})
{
p.cyclic=true;
walk ow;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
int rd=round(Srnd());
ow.p.push(p[rd]);
string R=dirs[rd];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
ow.nodes.push(tpos);
pos=tpos;
nextdir();
}
return ow;
}

walk randWalk(int Srnd(), int n, real angle=90, pen[] p={currentpen})
{
real R(){ return Srnd();}
return randWalk(R,n,angle,p);
}

void drawWalk(walk walk)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
real[][] depth;
for(int i=0; i < walk.nodes.length-1; ++i) {
real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=walk.nodes[round(depth[0][1])];
triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(walk.nodes[i]--walk.nodes[i+1],
abs(walk.nodes[i]-m)/abs(M-m)*walk.p[i]);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(Gaussrand,50000,new pen[] {red,yellow,blue}));
shipout(bbox(3mm,Fill));

```

Étiquettes :

## Random walk in the space – fig0050

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 15 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
import stats;
settings.render=0;

struct walk
{
triple[] nodes;
pen[] p;
}

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, B=backward, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, real angle=90, pen[] p={currentpen})
{
p.cyclic=true;
walk ow;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
int rd=round(Srnd());
ow.p.push(p[rd]);
string R=dirs[rd];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
ow.nodes.push(tpos);
pos=tpos;
nextdir();
}
return ow;
}

walk randWalk(int Srnd(), int n, real angle=90, pen[] p={currentpen})
{
real R(){ return Srnd();}
return randWalk(R,n,angle,p);
}

void drawWalk(walk walk)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
real[][] depth;
for(int i=0; i < walk.nodes.length-1; ++i) {
real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=walk.nodes[round(depth[0][1])];
triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(walk.nodes[i]--walk.nodes[i+1],
abs(walk.nodes[i]-m)/abs(M-m)*walk.p[i]);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(Gaussrand,1000,60,new pen[] {red,yellow,blue}));
shipout(bbox(3mm,Fill));

```

Étiquettes :

## Random walk in the space – fig0060

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 16 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
import stats;
settings.render=0;

struct walk
{
triple[] nodes;
pen[] p;
}

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, B=backward, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, real angle=90, pen[] p={currentpen})
{
p.cyclic=true;
walk ow;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
int rd=round(Srnd());
ow.p.push(p[rd]);
string R=dirs[rd];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
ow.nodes.push(tpos);
pos=tpos;
nextdir();
}
return ow;
}

walk randWalk(int Srnd(), int n, real angle=90, pen[] p={currentpen})
{
real R(){ return Srnd();}
return randWalk(R,n,angle,p);
}

void drawWalk(walk walk)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
real[][] depth;
for(int i=0; i < walk.nodes.length-1; ++i) {
real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=walk.nodes[round(depth[0][1])];
triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(walk.nodes[i]--walk.nodes[i+1],
abs(walk.nodes[i]-m)/abs(M-m)*walk.p[i]);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(Gaussrand,10000,60,new pen[] {red,yellow,blue}));
shipout(bbox(3mm,Fill));

```

Étiquettes :

## Random walk in the space – fig0070

Category: Asymptote,Examples 3D,Random Walk (3D)Ph. Ivaldi @ 17 h 46 min

 (Compiled with Asymptote version 1.84svn-r4619)
```
import three;
settings.render=0;

struct walk
{
triple[] nodes;
pen[] p;
}

string[] dirs={"U","D","B","F","R","L"};
// U=up, D=down, F=forward, R=right, L=left
dirs.cyclic=true;

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, real angle=90, pen[] p={currentpen})
{
p.cyclic=true;
walk ow;
triple udir=Z, vdir=X, kdir=cross(udir,vdir);
triple pos=O, tpos;
void changedir(real angle, triple axe)
{
transform3 T=rotate(angle,axe);
udir=T*udir;
vdir=T*vdir;
kdir=T*kdir;
}
void nextdir()
{
int rd=round(Srnd());
ow.p.push(p[rd]);
string R=dirs[rd];
if(R == "R") changedir(-angle,kdir);
else if(R == "L") changedir(angle,kdir);
else if(R == "U") changedir(angle,vdir);
else if(R == "D") changedir(-angle,vdir);
else if(R == "B") changedir(180,udir);
}
for (int i=0; i < n; ++i) {
tpos=pos+udir;
ow.nodes.push(tpos);
pos=tpos;
nextdir();
}
return ow;
}

walk randWalk(int Srnd(), int n, real angle=90, pen[] p={currentpen})
{
real R(){ return Srnd();}
return randWalk(R,n,angle,p);
}

void drawWalk(walk walk)
{
triple camera=currentprojection.camera;
if(currentprojection.infinity)
camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
real[][] depth;
for(int i=0; i < walk.nodes.length-1; ++i) {
real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
depth.push(new real[] {d,i});
}
depth=sort(depth);
triple M=walk.nodes[round(depth[0][1])];
triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
// Draw from farthest to nearest
while(depth.length > 0) {
real[] a=depth.pop();
int i=round(a[1]);
draw(walk.nodes[i]--walk.nodes[i+1],
abs(walk.nodes[i]-m)/abs(M-m)*walk.p[i]);
}
}

size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(rand,10000,60,new pen[] {red,yellow,blue}));
shipout(bbox(3mm,Fill));

```

Étiquettes :