SynapticMatter

A name with possibilities.

One starting node produces three later states

Use four abstract nodes A, B, C and D. The only directed connections are A to B, A to C, B to D and C to D. At step zero, only A is active. For each new step, a node becomes active if at least one of its incoming neighbours was active in the previous step. There is no persistence: a node without such input becomes inactive. Compute all new states simultaneously from the previous snapshot. This is a fictional discrete graph model, not a biological simulation.

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Compute the first simultaneous update in the SynapticMatter signal-step worksheetDirected edges: A → B · A → C · B → D · C → DStep 0 active: AStep 1 active: B and CD is not active yet at step 1Each update reads only the previous snapshot

01

Use the initial snapshot to compute the first update

At step zero the active set is A alone. Its two outgoing connections provide input to B and C, so those two nodes are active at step one. A has no incoming connection and becomes inactive. D receives no qualifying input from the step-zero snapshot because B and C were both inactive then. The step-one active set is therefore B and C. Do not use their newly computed activity to activate D within that same update; doing so would mix the old and new snapshots and violate the stated simultaneous rule.

Aggregate signals at one destination in the SynapticMatter signal-step worksheetStep 1 has two active sources: B and CTwo incoming signals reach DStep 2 has one active destination: DStep 3 active: noneTwo signals do not create two destination nodes

02

Combine incoming signals without duplicating the node

At step one, B and C are active. Each has a directed connection to D, so D receives two incoming signals for the next update. The rule only asks whether at least one exists. D is therefore one active node at step two, not two copies of a node. B and C become inactive because A was inactive in the step-one snapshot. At step three, no node has an active incoming neighbour: D has no outgoing connections, so the active set becomes empty. Count incoming signals and active destinations separately to avoid confusing two different quantities.

Retain the assumptions with the trace in the SynapticMatter signal-step worksheetPreserve the full modelNo persistence · simultaneous updatesTrace: A → {B,C} → D → emptyThe empty state stays empty under these rulesAbstract graph exercise, not a biological simulation

03

Save the model and its complete short trace

The worksheet records node identifiers, directed edges, the initial active set, the activation condition, the timing convention and whether activity persists. Its trace is A, then B and C, then D, then the empty set. Under these rules, the empty state remains empty on later steps. If activity were retained automatically, or if D had a connection back to A, the trace could change. Record either modification as a new model rather than describing it as a correction to this one. Keeping the full specification beside the trace allows another reader to reconstruct every update.

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