For each fraction p/q in lowest terms, erect a sphere of radius 1/(2q²) tangent to the plane at (p/q, 0). Drag to rotate.
Ford circles (1938): For each p/q in lowest terms, a circle of radius 1/(2q²) tangent to the x-axis at (p/q, 0). Two Ford circles are externally tangent iff |p₁q₂−p₂q₁|=1 (Farey neighbours). Ford spheres extend this to Gaussian integers: for (a+bi)/(c+di) with gcd=1, a sphere of radius 1/(2|c+di|²). The arrangement encodes the Stern–Brocot tree geometry and the modular group PSL(2,ℤ).