How to use this simulation
Choose the matrix size and number of memories; the grids update automatically. Click or drag across their squares to draw binary patterns. Restart simulation restores the defaults. The network stores all patterns in one shared set of connections.
Noise randomly flips the selected percentage of squares to create a starting cue. You can then click or drag across any noisy cue to change it before recall. The label reports its actual difference from the stored memory; regenerating the cues draws fresh random noise and discards those edits.
During animated recall, inspect the edited noisy cue, start the animation, and watch asynchronous neuron updates move the network toward a stable pattern. Click again to reveal the next noisy cue.
The final-state table reports the Hamming distance—the number of different cells—from every stored memory and its inverse. Previous memory and Next memory move directly among completed results without playing their animations. New update order reruns the same edited cues with a fresh random sequence while keeping the currently selected memory.
The energy is the network’s Lyapunov function. It should fall or remain level during asynchronous updates as the network approaches a stable attractor. With excessive noise, too many memories, or very similar memories, recall can fail or settle into a spurious pattern.
Model: a binary Hopfield network with standard 1/N-normalized Hebbian weights and asynchronous updates. Regenerating cues draws fresh noise; each recall uses a fresh update order. Reference: Hopfield, PNAS (1982). John J. Hopfield later shared the 2024 Nobel Prize in Physics for foundational work enabling machine learning with artificial neural networks.