Math resonance-flow diagrams
These diagrams describe conceptual flows you can render as SVG, Mermaid, or other formats.
Diagram 1 – Triadic sequence (Problem 1)#
Nodes:
- Triadic operator: $$D_3$$
- Exponent node: $$n$$
- Resonant-time: $$τ_r$$
- Output: $$a_n = D_3^n τ_r$$
Flow:
- $$D_3$$ flows into a power node with exponent $$n$$.
- Output multiplies $$τ_r$$.
- Final node outputs $$a_n$$.
- A control arrow adjusts $$τ_r$$.
Diagram 2 – Resonant integral (Problem 2)#
Nodes:
- Constant integrand: $$T_f D_6$$
- Integration bounds: $$0 \to τ_r$$
- Output: $$I = T_f D_6 τ_r$$
Flow:
- A constant node labeled $$T_f D_6$$ enters an integration block.
- Integration bounds are shown as $$0$$ and $$τ_r$$.
- Output is $$I$$.
Diagram 3 – Exponential resonance (Problem 3)#
Nodes:
- Composite constant: $$X$$
- Exponential node: $$e^{ΛΘ t}$$
- Triadic constant: $$D_9$$
- Solve-for node: $$t$$
Flow:
- $$X$$ multiplies the exponential.
- Output equals $$D_9$$.
- A “solve” node isolates $$t$$.
- A feedback arrow adjusts $$ΛΘ$$.