In this case noise() is probably better suited, because it can create smoother movement.

It now adds a point to the history every 10th frame. Play around with those two lines to finetune it as you like.

Code Example

1. ArrayList history = new ArrayList();
2. float distthresh = 60;
3. float factor = 2;
4.  
5. void setup() {
6.   size(800,500);
7.   background(255);
8.   strokeCap (SQUARE);
9.   strokeJoin(MITER);
10.   smooth();
11. }
12.  
13. void draw() {
14.   stroke(0,random(100,200));
15.   strokeWeight (random(0.2,0.8));
16.   animate();
17. }
18.  
19. void animate() {
20.   PVector d = new PVector(noise(frameCount*0.01)*width,noise(frameCount*0.005 + 3)*height,0);
21.   if (frameCount % 10 == 0) { history.add(0,d); }
22.  
23.   for (int p=0; p<history.size(); p++) {
24.     PVector v = (PVector) history.get(p);
25.     float joinchance = p/history.size() + d.dist(v)/distthresh;
26.     if (joinchance < random(0.5,factor))  line(d.x,d.y,v.x,v.y);
27.   }
28. }
29.  
30. void keyPressed() {
31.   if (key == 'c') {
32.     background(255);
33.     history.clear();
34.   }
35. }