Apollonian circle packing

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The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-2, 2, 2, -2]});
solveQ2 = function(x1,x2,x3,off) {
var a, b, c, d;
a = 0.5;
b = -(x1+x2+x3);
c = x1*x1+x2*x2+x3*x3-0.5*(x1+x2+x3)*(x1+x2+x3)-off;
d = b*b-4*a*c;
if (Math.abs(d)<0.00000001) d = 0.0;
return [(-b+Math.sqrt(d))/(2.0*a),(-b-Math.sqrt(d))/(2.0*a)];
}
 
a = brd.create('segment',[[0,0],[2,0]],{visible:false});
p1 = brd.create('glider',[1.3,0,a],{name:'Drag me'});
b0 = -0.5;
 
c0 = brd.create('circle',[[0,0],Math.abs(1.0/b0)],{strokeWidth:1});
c1 = brd.create('circle',[p1,function(){return 2-p1.X();}],{strokeWidth:1});
 
c2 = brd.create('circle',[[function(){return p1.X()-2;},0],function(){return p1.X();}],{strokeWidth:1});
c0.curvature = function(){ return b0;}; // constant
c1.curvature = function(){ return 1/(2-p1.X());};
c2.curvature = function(){ return 1/(p1.X());};
 
thirdCircleX = function() {
var b0,b1,b2,x0,x1,x2, b3,bx3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
x0 = c0.midpoint.X();
x1 = c1.midpoint.X();
x2 = c2.midpoint.X();
 
b3 = solveQ2(b0,b1,b2,0);
bx3 = solveQ2(b0*x0,b1*x1,b2*x2,2);
return bx3[0]/b3[0];
}
thirdCircleY = function() {
var b0,b1,b2,y0,y1,y2, b3,by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
y0 = c0.midpoint.Y();
y1 = c1.midpoint.Y();
y2 = c2.midpoint.Y();
 
b3 = solveQ2(b0,b1,b2,0);
by3 = solveQ2(b0*y0,b1*y1,b2*y2,2);
return by3[0]/b3[0];
}
thirdCircleRadius = function() {
var b0,b1,b2, b3,bx3,by3;
b0 = c0.curvature();
b1 = c1.curvature();
b2 = c2.curvature();
b3 = solveQ2(b0,b1,b2,0);
return 1.0/b3[0];
}
 
c3 = brd.create('circle',[[thirdCircleX,thirdCircleY],thirdCircleRadius],{strokeWidth:1});
c3.curvature = function(){ return 1.0/this.radius;};
 
otherCirc = function(circs,level) {
var c, fx,fy,fr;
if (level<=0) return;
fx = function() {
var b,x,i;
b = [];
x = [];
for (i=0;i<4;i++) {
b[i] = circs[i].curvature();
x[i] = circs[i].midpoint.X();
}
 
b[4] = 2*(b[0]+b[1]+b[2])-b[3];
x[4] = (2*(b[0]*x[0]+b[1]*x[1]+b[2]*x[2])-b[3]*x[3])/b[4];
return x[4];
}
fy = function() {
var b,y,i;
b = [];
y = [];
for (i=0;i<4;i++) {
b[i] = circs[i].curvature();
y[i] = circs[i].midpoint.Y();
}
 
b[4] = 2*(b[0]+b[1]+b[2])-b[3];
y[4] = (2*(b[0]*y[0]+b[1]*y[1]+b[2]*y[2])-b[3]*y[3])/b[4];
return y[4];
}
fr = function() {
var b,i;
b = [];
for (i=0;i<4;i++) {
b[i] = circs[i].curvature();
}
b[4] = 2*(b[0]+b[1]+b[2])-b[3];
if (isNaN(b[4])) {
return 1000.0;
} else {
return 1/b[4];
}
}
c = brd.create('circle',[[fx,fy],fr],{strokeWidth:1,name:'',
fillColor:JXG.hsv2rgb(50*level,0.8,0.8),highlightFillColor:JXG.hsv2rgb(50*level,0.5,0.8),fillOpacity:0.5,highlightFillOpacity:0.5});
c.curvature = function(){ return 1/this.radius;};
 
// Recursion
otherCirc([circs[0],circs[1],c,circs[2]],level-1);
otherCirc([circs[0],circs[2],c,circs[1]],level-1);
otherCirc([circs[1],circs[2],c,circs[0]],level-1);
return c;
}
 
//-------------------------------------------------------
brd.suspendUpdate();
level = 4;
otherCirc([c0,c1,c2,c3],level);
otherCirc([c3,c1,c2,c0],level);
otherCirc([c0,c2,c3,c1],level);
otherCirc([c0,c1,c3,c2],level);
brd.unsuspendUpdate();

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