Lorenz Attractor
Lorenz Attractor is a deterministic chaotic system.
For the physical significance, The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth , with an imposed temperature difference , under gravity , with buoyancy , thermal diffusivity , and kinematic viscosity .
This particular plot is x and z coordinates of Lorenz Attractor.
The attractor is described by the following system of differential equations:
$$\displaystyle\frac{{\left.{d}{x}\right.}}{{\left.{d}{t}\right.}}={a}{\left({y}-{x}\right)}$$
$$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{t}\right.}}={x}{\left({b}-{z}\right)}-{y}$$
$$\displaystyle\frac{{\left.{d}{z}\right.}}{{\left.{d}{t}\right.}}={x}{y}-{c}{z}$$
Code
elem=document.querySelector(".example-container");
setCanvas(elem);
x=0.01;
y=0.01;
z=0.01
a=10;
b=28;
c=8/3;
px=x;
py=y;
pz=z;
points=[];
function draw() {
clearCanvas();
dt=0.01;
dx= (a*(y-x))*dt;
dy= (x*(b-z)-y)*dt;
dz= (x*y - c*z)*dt;
x=x+dx;
y=y+dy;
z=z+dz;
points.push([WIDTH/2+8*x,3*HEIGHT/4-5*z]);
new polygon(points,'#696969',0,'#695fe6',0.7,false);
px=x;
py=y;
pz=z;
requestAnimationFrame(draw);
}
draw();