Biology resonance-flow diagrams

This file describes conceptual diagrams you can render as SVG, Mermaid, or other tooling.

Diagram 1 – Resonant cell growth pipeline (Problem 1)#

Nodes:

• Initial population node: $$G_0$$
• Resonant-time node: $$τ_r$$
• Triadic growth node: $$D_3$$
• Exponential growth node: $$e^{D_3 τ_r t}$$
• Output node: $$G(t)$$

Flow:

1. $$G_0$$ (initial cells) flows into a multiplier node.
2. $$τ_r$$ feeds into a triadic node labeled $$D_3$$, producing $$D_3 τ_r$$.
3. That value is sent into an "Exponential" node $$\exp(\cdot t)$$, giving $$e^{D_3 τ_r t}$$.
4. The exponential output multiplies $$G_0$$ to yield $$G(t)$$.

You can add a control arrow from a "Environment" node to $$τ_r$$, indicating how environmental changes alter resonant-time and growth.

Diagram 2 – Protein folding stability loop (Problem 2)#

Nodes:

• Environment node: $$Λ$$
• Temperature node: $$Θ$$
• Destabilizing node: $$D_9$$
• Stability node: $$P = ΛΘ / D_9$$

Flow:

1. $$Λ$$ and $$Θ$$ merge at a "Coupling" node to form $$ΛΘ$$.
2. $$D_9$$ enters a division node along with $$ΛΘ$$.
3. The division node outputs $$P$$.
4. A "Noise" node points into $$D_9$$ to represent stress-induced destabilization.
5. A feedback arrow from $$P$$ back to $$Θ$$ shows regulatory attempts to maintain stability by adjusting temperature or chaperone activity.

Diagram 3 – Neural oscillation coupling (Problem 3)#

Nodes:

• Structural network node: $$D_6$$
• Elevation node: $$T_f$$
• Frequency node: $$f_n = T_f D_6$$
• State node: "High attention" requiring $$f_n' = 1.15 f_n$$

Flow:

1. $$D_6$$ (fixed structure) feeds into a multiplier node.
2. $$T_f$$ (adjustable neuromodulatory state) also feeds into the same node.
3. The product node outputs $$f_n$$.
4. A "High-attention demand" node specifies $$f_n' = 1.15 f_n$$.
5. A feedback arrow adjusts $$T_f$$ until $$f_n'$$ meets the demanded value.

You can visually encode that only $$T_f$$ is tunable, while $$D_6$$ is a fixed structural property.