Transcript Drawing Apollonian Circle Packings

Drawing Apollonian Circle
Packings
Complex Descartes’ Theorem
• a2 + b2 + c2 + d2 = ½(a + b + c + d)2
• (b1z1) 2 + (b2z2) 2 + (b3z3) 2 + (b4z4) 2 = ½(b1z1 +
b2z2 + b3z3 + b4z4) 2
• bj = curvature
zj = x + yi
Apollonius’ Theorem
MATLAB in action!
Other Apollonian Circle Packings
Apollonian Circle Packings with First Four Curvatures: -2, 3, 6, 7
Geogebra!
More curvatures
3D!