The fundamental principle that connects all of these examples is self-similarity across scales, a key feature of fractals. Fractals are complex patterns that exhibit similar structures at different levels of magnification or scale. They are created by repeating a simple process or mathematical formula over and over in a recursive, iterative manner.

In general terms, a fractal is a geometric object that satisfies two criteria:

1. Self-similarity: The structure appears similar at different scales. Small parts of the object resemble the whole.

2. Infinite detail: As you zoom in on the object, more and more detail emerges, and this detail resembles the larger-scale structure.

The given examples exhibit fractal-like properties:

1. A river delta: The branching patterns of the river channels resemble the overall structure of the delta at different scales.

2. The branching structure of a lightning bolt: The smaller branches of the lightning bolt resemble the larger structure of the entire bolt.

3. The vascular system of a leaf: The smaller veins of the leaf resemble the larger veins and the overall structure of the leaf's vascular system.

4. A hierarchical corporate management structure: The smaller departments or teams within the company often resemble the larger structure of the entire organization.

Another completely different example of a system that exhibits fractal-like properties is the coastline of a country or continent. When you view a coastline from space, it appears jagged and irregular. As you zoom in closer, the coastline reveals more and more detail, with smaller bays, peninsulas, and inlets that resemble the larger-scale structure of the entire coastline. This self-similarity across scales and the infinite detail that emerges as you examine the coastline more closely are characteristic of fractals.