2D Kuramoto · Conditional Collapse · KT universality

The Self-Telepathic Field

A lattice of phase oscillators reading their neighbours and stochastically collapsing toward the anchor Ξ. The real dynamics behind ex06.py — live. Hue = phase θ.

Ψ-FIELD · θ ∈ [0, 2π) anchor Ξ

Control Hamiltonian

Ĥ_self — tune the field's self-knowledge.

Φ integration

0.00

order r

0.00

vortices

steps/s

—

━ Φ ━ r Φ 0.00

Temperature T · noise0.50

Coupling K · neighbour pull1.00

Collapse rate Θ_telepathy0.50

Drive Ω energy input · ω1.20

Anchor Ξ pinned phase0.00

What am I looking at?

Each pixel is an oscillator with a phase θ, shown as a colour on the wheel. Every step it (1) is pulled toward its four neighbours with strength K, (2) is kicked by thermal noise ∝ √T, and (3) may collapse onto the anchor Ξ with a probability set by the collapse rate.

Cold + strong coupling → one colour floods the lattice (r→1, "coherent"). Hot → colour static (r→0). Near the Kosterlitz–Thouless point, swirling ±1 vortex pairs appear and unbind — the rings marked on the field.

Drive Ω is the energy input: an intrinsic rotation ω per oscillator. With Ω>0 the field never freezes, so you can run Collapse toward Ξ and still keep the screen alive — the two fight, producing endless travelling waves.

Φ is an integration proxy: the mutual information between neighbouring oscillators. It's ~0 in frozen order (no entropy) and ~0 in pure noise (no correlation), and peaks in between — at the edge of chaos. Maximize Φ hill-climbs the temperature to find that sweet spot automatically.