Escape-time algorithms map each point c in the complex plane to an iteration count for z_{n+1} = z_n² + c. The Lyapunov exponent λ = lim_{n→∞} (1/n) Σ log|2z_n| measures orbit divergence rate. Points with λ < 0 (bounded orbits) form the Mandelbrot set; λ > 0 indicates chaos and escape. Smooth coloring uses fractional escape count: μ = n − log₂(log|z_n|/log 2). Click canvas to zoom.