Processing

float noiseScale= 0.005;
float noiseOffsetX;
float noiseOffsetY;

void setup (){

  size(800, 600, P2D);
  background(255);
  smooth();
  noFill();
  stroke(0,0,0,32);
  for (int i = 0;1<300;i++){
    noiseOffsetX += 5;
    noiseOffsetY += 7.1;
    drawOneStream();
  }
}

void drawOneStream(){
 float px = 0;
 float py = height/2.0;
 float vx = 1;
 float vy = 0;
 int pcnt = 0;
 while ((px>=0) && (px<width) && (py<height) && (py>=0)){
  point(px,py);
 float xNoise = noise((pcnt+noiseOffsetX)*noiseScale);
 float yNoise = noise((pcnt+noiseOffsetY)*noiseScale);
 vx = ((2+vx)+1+map(xNoise,0,1,-1,1))/4.0;
 vy = ((3*vy) +map(yNoise,0,1,-1,1))/4.0;
 px += vx;
 py += vy;
 pcnt++;

 }
}