Holographic thoughts, made visible — every pixel computed, nothing canned.
Five live simulations of the membrane models: projection recall, the yin–yang predictive loop, Hebbian crystallization, the refusing gate, and the capacity limit where the record shatters. Phase is hue; magnitude is brightness.
Sixteen complex oscillators hold four stored patterns — thoughts. A noisy probe is sent in; recall is pure projection: the field keeps only the part of the probe that lies in the span of the stored patterns, and the overlaps mi = ⟨pi|probe⟩ decide which thought it was. Watch the ring morph from noise back into a thought.
Live toy simulation in your browser — see the Python models (yin-yang-membranes, membrane-crystallization, refusing-membrane, quantum-projection, membrane-capacity) for the measured numbers. Recall here is one-shot projection onto the stored patterns — the same operation the Python quantum-projection model measures.
Two rings of 48 phase oscillators chase conjugate traveling waves. Each membrane is pulled toward its own pattern and toward its partner: yin reads yang's present shape error, yang reads yin's predicted next state — the asymmetric “tic”. Dot color is tracking error: cyan = locked, red = lost. Destroy yang and watch whether yin can resurrect it through the loop.
Live toy simulation in your browser — see the Python models (yin-yang-membranes, membrane-crystallization, refusing-membrane, quantum-projection, membrane-capacity) for the measured numbers. Python reference (yin-yang-membranes, seeds 7/21/42): at κ = 0.45 coupling lowers joint overlap, 0.78–0.79 vs 0.90 alone (intact) and 0.45–0.46 vs 0.72 alone (amnesia); a destroyed yang relocks in 2–3 ticks coupled and 2–4 alone, and under amnesia coupling slows recovery (58–658 ticks vs 4–9 alone; one alone run did not recover). A negative result.
A stream of noisy observations — three Bell-state patterns in 8 dimensions, arriving with frequencies 0.6 / 0.3 / 0.1 — is folded into a memory matrix by Hebbian updates, W ← (1−α)W + α|x⟩⟨x|. The spectrum of W is eigendecomposed live. Crystallization is not “entropy falls”: watch the top-3 eigenvalues separate, the subspace fidelity climb, and the leftover residue turn white — structure extracted, noise left behind.
Live toy simulation in your browser — see the Python models (yin-yang-membranes, membrane-crystallization, refusing-membrane, quantum-projection, membrane-capacity) for the measured numbers. Python reference (membrane-crystallization, σ 0.25): subspace fidelity 0.96–0.97; residue whiteness 0.993 (not discriminative: pure noise scores 0.995); self-recreation match fidelity 0.953 → 0.798 from generation 1 to 5.
Four patterns live in the library: GHZ, W, |000⟩, |+++⟩. A probe is accepted only if its best overlap clears a threshold τ. First calibrate: 200 labeled probes (half noisy library members, half random strangers) sweep τ to maximize Youden's J — then τ freezes. Stream probes and watch the gate decide; raise σ to 0.5 and feel distribution shift.
Live toy simulation in your browser — see the Python models (yin-yang-membranes, membrane-crystallization, refusing-membrane, quantum-projection, membrane-capacity) for the measured numbers. Python reference (refusing-membrane): τ = 0.700, accuracy-on-accepted 0.995; under distribution shift (σ 0.25 → 0.50) it caught 75.6% of new errors.
One membrane of N = 64 complex oscillators stores P random patterns by the outer-product rule W = Σ|p⟩⟨p|. A noisy probe is recalled by the multiply itself: y = W · probe, then classified by argmax |⟨pi|y⟩|. Crosstalk between random patterns sets a floor (~1/√N); noise and load push accuracy over the edge. Watch the 8×8 grid morph from probe to recall, then sweep P until the record shatters.
Live toy simulation in your browser — same outer-product holographic-memory family and capacity story as membrane-capacity, not the identical classifier: here recall is y = W·probe then argmax |⟨p|y⟩|; the Python repo classifies by direct one-shot projection, argmax |⟨p|probe⟩|. Measured numbers live in the Python repo. Python reference (membrane-capacity): crosstalk floor for N=64 is 0.1102 vs theory √(π/4N)=0.1108 (0.5% off); at σ=0.15 classification accuracy held at 1.000 out to P=1024; at σ=0.30 P90=4 (grid coarseness: true P90 between 4 and 8). Capacity is bought with quiet, not size.