Catholic Church

With 1.3 billion members globally, the Catholic Church operates the oldest continuously functioning fractal organizational structure (~2,000 years). The Church's hierarchy branches from the Pope through Cardinals, Archbishops, Bishops, Priests, to Parishes - a self-similar structure enabling centralized doctrine with localized implementation across continents and centuries.

The fractal enables one-to-billions communication with only 5-6 hierarchical layers - logarithmic scaling. Each level manages ~5-15 direct reports, balancing control with efficiency. However, the structure's rigidity creates challenges as reforms take decades to permeate to parishes.