A fulcrum — the dot — with four 90° quadrant-windows hinged on it: [0,90] [90,180] [180,270] [270,360], bracketed by α (start) and Ω (end) — the same point, because a full turn comes home (360 = 0). And it's fractal: each quadrant is itself a fulcrum of four. Click any quadrant to descend — the count climbs by powers of four.
The dot is the fulcrum — the pivot. Hinged on it are four quadrants, each a 90° window: [0,90], [90,180], [180,270], [270,360]. Four times ninety is three-sixty exactly — the rotation tiles with no remainder. α opens it at 0; Ω closes it at 360 — and Ω is α, because the turn returns home.
90° is the right angle — the natural quantum of a fulcrum's rotation, the cardinal split. Four quadrants tile a full turn exactly, no remainder, no overlap. Base 4 isn't chosen here; it's what a rotation gives you when cut at its natural division — the way 2 is natural for a switch and 3 for the balanced −1/0/+1. Base 4 = the rotation cut at right angles.
Each quadrant, zoomed, is a whole fulcrum — four sub-quadrants on its own sub-pivot, with its own α and Ω. So the structure is self-similar: every node fans into four, each of those into four, forever. The count is 4ⁿ:
| Depth | Nodes | Power |
|---|---|---|
| 0 | 1 | 4⁰ (the fulcrum) |
| 1 | 4 | 4¹ |
| 2 | 16 | 4² |
| 3 | 64 | 4³ |
| n | 4ⁿ | 4ⁿ |