Overview
Wave propagation is one of the first emergent phenomena of the Recursive Emergent Mechanics (REM) Framework. It arises naturally from the recursive interaction of neighbouring nodes and does not require a separate wave equation or propagation algorithm.
Within the REM Framework, a wave is the recursive propagation of a local mechanical disturbance through the lattice. Each node responds only to the positions of its directly connected neighbouring nodes. As neighbouring nodes update their mechanical state, the disturbance is transferred recursively from one neighbourhood to the next.
Wave propagation is therefore not an independent mechanism. It is a direct consequence of the Fundamental Node Equation and the Recursive Node Dynamics described in the preceding articles.
Local Mechanical Disturbances
A wave begins when one or more nodes are displaced from their local equilibrium. This displacement creates a mechanical imbalance within the surrounding neighbourhood.
During the following recursive update, neighbouring nodes measure this imbalance and compute restoring accelerations using the Fundamental Node Equation. Their resulting motion then modifies the mechanical balance experienced by the next neighbouring nodes.
Rather than remaining localized, the disturbance is therefore transmitted recursively throughout the lattice. Every node participates only through local interactions, yet the collective behaviour produces the propagation of a mechanical wave across the lattice.
Propagation Through Recursive Updates
Mechanical disturbances propagate because every recursive update transfers the local mechanical imbalance from one neighbourhood to the next. No node transmits information directly over long distances, and no global coordination exists within the lattice.
Instead, each node responds only to the current mechanical state of its neighbouring nodes. The updated node state then becomes part of the neighbourhood evaluated during the next recursive update. Repeated execution of this process advances the disturbance through the lattice.
Wave propagation therefore emerges entirely from the recursive application of local mechanical interactions.
Wave Speed
The speed of a mechanical wave is determined by the recursive transfer of local mechanical disturbances between neighbouring nodes. During each recursive update, every node responds to the current state of its directly connected neighbours. The collective effect of these local interactions determines how quickly a disturbance propagates through the lattice.
Unlike continuous wave models, the REM Framework does not assume an independently defined wave velocity. Instead, wave propagation emerges directly from the recursive update cycle governed by the Fundamental Node Equation.
The propagation speed depends on the mechanical parameters of the recursive lattice. In the current implementation, a configurable wave-speed constant determines the magnitude of each velocity update and therefore controls the speed at which disturbances travel through the lattice.
Changing this parameter alters the propagation speed without modifying the underlying recursive mechanics. The mechanism responsible for wave propagation remains identical; only the rate at which recursive updates transfer the disturbance changes.
Wave Interference
One of the earliest demonstrations of the REM Framework was the emergence of wave interference. When multiple mechanical disturbances propagate simultaneously through the lattice, every node continues to apply exactly the same local recursive update rule.
Because each node responds only to the combined mechanical state of its neighbouring nodes, overlapping disturbances naturally interact. No additional interference algorithm is introduced, and no node distinguishes between individual wave sources.
The resulting behaviour produces regions where local disturbances reinforce one another as well as regions where they reduce one another. These interference patterns emerge solely from the recursive mechanics of the lattice.
Wave interference is therefore not an independent phenomenon added to the simulation. It is a natural consequence of neighbouring nodes recursively responding to their local mechanical environment.
Constructive Interference
Constructive interference occurs when neighbouring disturbances combine to increase the local mechanical displacement. The resulting positional differences generate larger restoring accelerations, producing regions of increased wave amplitude.
Within the REM Framework, constructive interference emerges naturally whenever multiple disturbances reinforce the same local mechanical imbalance.
Destructive Interference
Destructive interference occurs when neighbouring disturbances reduce the local mechanical imbalance. As the positional differences become smaller, the resulting restoring accelerations are likewise reduced, producing regions of diminished wave amplitude.
Both constructive and destructive interference arise from the same recursive update mechanism. The REM Framework requires no additional rules to distinguish between them.
Emergent Wave Propagation
Within the REM Framework, wave propagation is not introduced as a fundamental law. Instead, it emerges naturally from the recursive interaction of neighbouring nodes. Every node follows exactly the same local mechanical rules, regardless of whether a wave is present.
The propagation of a wave is therefore not computed directly. It is the collective consequence of many local recursive updates performed throughout the lattice.
This distinction is fundamental. The REM Framework does not define a separate mechanism for wave propagation. The recursive mechanics of the lattice alone are sufficient to generate travelling mechanical disturbances.
Wave propagation is therefore an emergent property of the recursive lattice rather than an independent assumption of the framework.
Summary
Wave Propagation describes how local mechanical disturbances travel through the recursive lattice of the REM Framework. Every node responds exclusively to the relative positions of its directly connected neighbouring nodes, allowing disturbances to propagate recursively without any global coordination.
The lattice itself remains stationary while individual nodes oscillate around their local equilibrium positions. The travelling wave is therefore the propagation of a mechanical disturbance rather than the transport of the lattice itself.
Constructive and destructive interference emerge naturally from the recursive interaction of neighbouring disturbances. No additional propagation or interference rules are introduced beyond the recursive update cycle.
Wave propagation therefore represents one of the earliest emergent phenomena of the REM Framework and forms the mechanical foundation for the introduction of persistent oscillating identities in the following article.
Key Takeaways
- Wave propagation emerges naturally from recursive local interactions.
- The lattice remains stationary while mechanical disturbances propagate.
- Every node oscillates locally around its equilibrium position.
- No separate propagation algorithm is required.
- Constructive and destructive interference arise naturally from the same recursive mechanics.
- Wave propagation provides the foundation for persistent oscillating identities.