Read the equation
The function f converts a relative displacement into a pairwise contribution, and the sum aggregates contributions from other agents. To interpret the displayed result as motion, the source must specify whether it is a position, velocity, force, or increment. The adjacent scalar target tracker alone does not define a multi-agent swarm.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
## 3.10 Family 9: Swarm Interaction ``` f₉(x) = x + 0.05 · softsign(dx_norm - x) ``` **Equation Type**: Swarm force: x_i = Σ f(x_j - x_i) **Explanation**: Models attraction/repulsion dynamics between agents. The softsign creates bounded forces that prevent collapse or explosion. ## 3.11 Family 10: Field Accumulator ``` ρ = 1 / (1 + φ) f₁₀(x) = (1 - ρ) · x + ρ · dx_norm ```
Exact original notation
Swarm force: x_i = Σ f(x_j - x_i)