SPACE-TIME ELEVATOR

by @mrinreality1

What you’re looking at

A living field grown from two of nature’s most famous numbers held in balance: π, which governs circles and curvature, and φ, the golden ratio, which governs growth that copies itself - sunflower seeds, nautilus shells, galaxy arms. Everything on screen - every shell, fold and wave - comes from how these two shape each other. You fly through it: drag to orbit, pinch or scroll to descend. The descent never ends.

The balance point

π and φ come from completely different mathematical worlds, yet they meet at one quiet spot: the radius where a circle’s area is exactly golden.

First principles

• π - the circle-maker. The Swirl control. It bends the spiral shells and steers the folding that nests structure inside structure.
• φ - growth that remembers itself. The Growth control. φ is the only number whose square just adds one (φ² = φ + 1) and whose reciprocal just subtracts one (1/φ = φ − 1). That self-similarity is why it appears wherever things grow in proportion.
• ψ - the wave. The Waves control. Interfering ripples give the field its living texture; Breathe mode slowly cycles their phase.
• The bridge. One special exponent turns golden growth into circles: φ^d* = π, with d* ≈ 2.379. The field’s Density rests exactly there by default.
• The golden angle. Slicing a full turn by φ² gives ≈ 137.5° - the sunflower’s packing angle. Each time the elevator passes a fold-level, the wave phase quietly steps by exactly this angle.
• The surface level. Surfaces crystallize where density reaches 1/φ² ≈ 0.382 of full - the same golden fraction that sets the angle above.

The elevator

Depth here is measured in φ-layers: every ×φ of zoom is one floor. Nature runs the same ladder - from the Planck length up to the observable universe is about 294 φ-layers, passing protons, DNA, cells, you, Earth, and galaxies on the way. In this field the ride is endless: the folded pattern re-seeds itself as you fall, so there is always another floor. The metrics panel shows your current layer. The Elevator W slider is a fourth axis - slide it (or engage Auto Elevator) to glide between parallel cross-sections of the field.

Flying it

• Drag orbits with momentum · two-finger drag (or Shift/right-drag) pans the look-at centre. Both slow as the zoom ratio grows, so navigation stays precise no matter how deep you are.
• Pinch / scroll rides the elevator - endlessly in both directions: dive forever, or pull back forever as the whole bloom shrinks and the field re-seeds.
• Double-tap toggles auto-spin · Pause freezes field time but never your hands - orbit, pan and descend through a frozen instant.
• Control deck (bottom) - presets, the parameter tabs (including Coherence K), Marks (named bookmarks), and Capture & session (snapshot, video, share-link, export / import, and a return to genesis).
• Everything persists on this device - leave and you'll return exactly where you were. The share-link encodes your precise view, parameters, pan and depth. Press ? for the full keyboard map.

Color by coherence - a Kuramoto palette

Color spans the whole visible spectrum, but it isn’t sprayed on at random. At every point the shader seeds five tiny oscillators from the field itself - its rotation angle, its curvature (π), its growth (φ), its wave (ψ) and its radial slice. Local density sets the coupling K; a few steps of the Kuramoto equation let them try to synchronise. Where they lock, the region collapses onto one pure, aligned hue; where they can’t, the spectrum splays apart. So emergent shells, cells and filaments sort themselves into color, and coherent structure lights up plainly. The Coherence (K) slider turns this synchronisation up or down.

Under the hood

One self-contained file, no dependencies. Every frame is ray-marched: rays gather translucent density like light in nebular gas, surfaces catch rim and Fresnel light, and over-dense regions ignite gold. Iridescence rides on top of the coherence palette - interference rings band every form like thin film on a bubble, brightening where phases lock, while silent field falls to a truly dark void so spheres and hollows emerge on their own. The engine watches its own frame-rate and quietly retunes resolution and detail to stay fluid on any device.

Created by @mrinreality1 on X
Built on a single first principle - the π·φ equilibrium, where πr² = φ and φ^d* = π.

Key Map