var sc = 300;

var n = [0];//x coords for input points

var o = [0];//y coords for input points

var ns = 0; //storage copy of the x coords while the original is being manipulated

function setup() {//setup

  var x = 1;//ratio numerator

  var y = 5;//ratio denominator

  angleMode('radians');//makes sure everything is in radians

  frameRate(60);//sets the uh... theoretical frame rate

  createCanvas(1200, 1200);//makes the background

}

var n2 = 0;//x coords for output points

var o2 = 0;//y coords for output points

var e = 1;//x coord for first term in the möbius transform

var f = 3;//y coord for first term in the möbius transform

var g = -1;//x coord for first term in the möbius transform

var h = 0;//x coord for first term in the möbius transform

var j = 1;//x coord for first term in the möbius transform

var k = -2;//x coord for first term in the möbius transform

var l = 4;//x coord for first term in the möbius transform

var m = 0;//x coord for first term in the möbius transform

var p = 0;//variable for just like, compactness

var q = 0;//variable for just like, compactness

var r = 0;//variable for just like, compactness

var s = 0;//variable for just like, compactness

function draw() {

  background(0,0,0);

  var x = 1;

  var y = 5;

  var n = [0];

  var o = [0];

  var tuner = 5*PI/13/2;//why 5/13 works I haven't the foggiest, must be tuned for new values of x and y

  strokeWeight(2);

  stroke(0,255,0);

  t+=0.1;

  for(var i = -8; i<8; i+=1){    

    for(var j = -8; j<8; j+=1){

      for(var k = -10; k<11; k++){

        if(k%2==0){

        n.push(/*t+((mouseX-600)/sc)/2+*/(1*(i+0.5)/y+(j+k/20+0.5)/x)*(tuner));

        o.push(/*((mouseX-600)/sc)/2+*/(1*(i+0.5)/x-(t%(y*y+x*x)+j+k/20+0.5)/y)*(tuner));

        }

        else{

        n.push(/*t+((mouseX-600)/sc)/2*/(1*(i+k/20+0.5)/y+(j+0.5)/x)*(tuner));

        o.push(/*((mouseY-600)/sc)/2*/(1*(i+k/20+0.5)/x-(t%(y*y+x*x)+j+0.5)/y)*(tuner));

        }//it took me about 6 hours+ to get this semi-worked out

        ns=n[n.length-1];

        point(600+ns*sc,600+o[o.length-1]*sc);

        n[n.length-1] = pow(2.7182818,ns)*cos(o[o.length-1]);

        o[o.length-1] = pow(2.7182818,ns)*sin(o[o.length-1]);

      }

    }

  }

  for(var i=0; i<n.length; i++){

    stroke(255,0,0);

    point(600+n[i]*sc,600+o[i]*sc);

    p = n[i]*f+o[i]*e+h;

    q = n[i]*k+o[i]*j+m;

    r = n[i]*e+g-o[i]*f;

    s = n[i]*j+l-o[i]*k;

    n2 =((((r*s)+(p*q))/(sq(s)+sq(q))));//it took me about an hour to find an error in my math here, good gosh

    o2 =((((p*s)-(r*q))/(sq(s)+sq(q))));

    stroke(0,0,255);

    point(600+n2*sc,600+o2*sc);

  }

}