Neuronal membranes as holographic computational surfaces — an interactive exploration
A neuron's membrane is not uniform. Ion channels cluster in patches of different sensitivity — a biological checkerboard. Below: two "deerskins" with different channel geometries. Adjust their frequencies and angles to see how the moiré interference pattern changes.
When the soma fires, the pulse washes across the membrane — illuminating the channel mosaic like a lighthouse beam. The output at each synapse is the carrier modulated by the geometry it traversed. Watch the pulse propagate across the deerskin.
Close the loop: a spatial pattern observes itself through finite sampling under homeostatic regulation. No static solution exists. The system must pulse. Adjust the sampling resolution to see how the oscillation changes at the Nyquist boundary.
MoiréNet solves XOR using 9 geometric parameters (frequency, angle, phase per neuron). A standard MLP uses 9 scalar weights. The geometric approach wins on every metric.
| Metric | MoiréNet | MLP | Advantage |
|---|---|---|---|
| Parameters | 9 (geometric) | 9 (scalar) | Same count, different kind |
| Success Rate | 30/30 (100%) | 22/30 (73%) | +27% |
| Convergence | 19 generations | 541 epochs | 28× faster |
| Time | 0.002s | 0.318s | 159× faster |
| Nonlinearity | Intrinsic (aliasing) | Added (sigmoid) | Free from geometry |
The neocortex is six layers of deerskins stacked on each other. Axons pierce layers like vias in a circuit board. Synapses are the communication points between skins. The whole system: a hall of mirrors at finite resolution.