Here is my Processing sketch of Random Walk applied with Gaussian Distribution. Each step is connected to a current mouse position, and color of each step changes according to the mouse position; I used colorMode(HSB, height, height, height). My main purpose of this project was to apply mathematical concept to a method of drawing rainbow wave, perhaps rainbow lollipops since curves connected to ellipses look like a bunch of lollipops!

Screenshots

Code

Walker w;

void setup(){
size(800, 400);

w = new Walker();
background(0);

}

void draw() {

w.step();
w.render();

}

class Walker{
Random generator = new Random();

float prevX, prevY, x, y, randomNum;

Walker(){

//x = mouseX;
//y = mouseY;
x = random(50, width-50);
y = random(50, height-50);
colorMode(HSB, height, height, height);
}

void render(){
stroke(255);
//noStroke();
//point(x,y);

//line(prevX, prevY, x, y);

curve(x, y, x, y, mouseX, mouseY, mouseX-20, mouseY-20);
float mappedR = map(mouseX, 0, 800, 0, 255);
// fill(255, 255-mappedR, 255-mappedR);
fill(mouseY, height, height);
ellipse(x, y, 15, 15);

//line(prevX, prevY, x, y);

}

void step(){

//prevX =x;
//prevY =y;

float stepx = random(-1, 1);
float stepy = random(-1, 1);

float randomNum = (float)generator.nextGaussian();
//randomNum = montecarlo()*50;
stepx *= 10+randomNum;
stepy *= 10+randomNum;

x+= stepx;
y+= stepy;

//Stay on the screen
x = constrain(x, 0, width-1);
y = constrain(y, 0, height-1);

}

float montecarlo() {
while (true) {

float r1 = random(1);
float probability = pow(1.0 - r1,8);

float r2 = random(1);
if (r2 < probability) {
return r1;
}
}
}

}