Six spatial sine and cosine gratings encode three input frequencies × two output channels. The matrix is read from the bed, so erasing the bed erases what was learned.
04 / A matrix of living shores · interactive numerical AI
One beach remembers.
Four beaches think together?
Strong waves write persistent material. Weak waves ask questions. Channels let one beach address another. An explicit attention reader decides which memories matter. This is the bridge from wave-written geometry to fast-weight associative AI.
A genuine computational model, not a claim of artificial consciousness.
Each beach has 36 material cells and 36 fast water cells. Six spatial Fourier imprints encode a 3 × 2 matrix in the material. The browser computes writes, reads, network routing and attention from those states. A separate damped wave recurrence supplies the animated fast wave field.
01 / A network of four wave-written memories
Links open0 teaching eventsDelta rule · corrective writeContent-sensitive attention
Click a beach to choose where the next wave enters. Cyan is the fast field u(x,t); amber is the slow written material h(x). The six numbers below each beach are decoded from its material profile, not a hidden parallel weight array. Lines indicate available inter-beach routes.
Write a lesson / send a weak ping
Reading is nondestructive. Linked access and forwarding lessons are different toggles: a message arriving elsewhere does not by itself teach that beach.
What did the memory answer?
Response vector[0.00, 0.00]
Largest outputRIGHT
← LEFT50.0%RIGHT →
Connected network. The confidence is a softmax of the two output components, not a calibrated probability of correctness.
Attention paid to each beach
A25%
B25%
C25%
D25%
02 / Does order actually enter the material?
Write LEFT then RIGHT into the same frequency and compare with RIGHT then LEFT on a fresh cloned beach. In an additive writer the two updates commute. A corrective writer uses what was already there, so order can matter.
No matched control run. Try it with Hebbian or Delta selected above; the experiment evaluates both writers under the same η.
Signals and changes
A strong teaching pulse changes the spatial coefficients. A weak ping reads the current coefficients; the fast wave animation propagates through links, but the mathematical memory readout is the Fourier projection of h.
03 / How a beach becomes an AI component
The math behind the metaphorA one-hot frequency selects a row of the stored matrix. Links let the query reach other memories, and content-dependent attention mixes their responses. A weak probe does not overwrite the bed.
Hebb adds a new imprint; the delta rule compares the desired answer with the old response and writes only that difference. A gated puddle could someday determine whether a physical write happens—but this page's gate is algorithmic.
h_b(x) = Σ_{key,value} W_b[key,value] φ_{key,value}(x)
W_b[key,value] = Σ_x h_b(x) φ_{key,value}(x) (orthonormal gratings)
local_read_b(q) = W_bᵀ q
Hebb: ΔW_b = η · key ⊗ target
Delta: ΔW_b = η · key ⊗ (target − W_bᵀ key)
network_read(q) = Σ_b attention_b(q, reachability) · W_bᵀ q
Where the analogy stops: The water recurrence genuinely propagates and the material genuinely stores the numeric matrix, but our attention and target-driven delta update are explicit software calculations. The readout is a Fourier projection of the bed—not an observed wave echo through that bed. No spontaneous physical teacher, autonomous objective, inverse-loss wave or neural tissue is demonstrated. A real version would require a mechanism to implement both the readout and update locally under loss and finite resources.