waddington-landscape
Waddington's epigenetic landscape: cell fate as gradient flow on potential surfaces, connecting developmental biology to dynamical systems, Schrödinger bridges, and fractional diffusion
Profile →npx skills add majiayu000/claude-skill-registry --skill waddington-landscape --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Waddington Landscape Skill > *"The cell is like a ball rolling down a landscape of valleys. Once it enters a valley, it is canalized toward a particular fate."* > — Conrad Hal Waddington (1957) ## Overview **Waddington's epigenetic landscape** is the foundational metaphor for developmental biology: | Concept | Landscape Metaphor | Mathematical Structure | |---------|-------------------|----------------------| | Cell | Ball/marble | State point θ(t) | | Differentiation | Rolling downhill | Gradient descent | | Cell fate | Valley bottom | Attractor basin | | Fate decision | Ridge/bifurcation | Critical point | | Landscape shape | Epigenetic regulation | Potential V(θ) | ## The Mathematics ### Gradient Flow on Potential Landscape ``` dθ/dt = -∇V(θ) + √(2T) dW(t) Where: θ = cell state (gene expression profile) V(θ) = epigenetic potential (landscape height) T = temperature (stochastic fluctuations) dW = Brownian motion (noise) ``` This is **Langevin dynamics** on the Waddington landscape! ### Connection to FDBM (NeurIPS 2025) The **Fractional Diffusion Bridge Models** paper (Nobis et al., 2025) provides the modern framework: ``` Standard Brownian (H=0.5): Memoryless diffusion No long-
- Overview
- The Mathematics
- Gradient Flow on Potential Landscape
- Connection to FDBM (NeurIPS 2025)
- Schrödinger Bridge Formulation
- Modelica Implementation
- Basic Landscape with Pitchfork Bifurcation
- Three-Fate Landscape (Stem Cell → Neuron/Muscle/Blood)
- Fractional Dynamics (MA-fBM)
- Python Implementation
- Waddington Landscape Class
- FDBM Integration
- Connection to Other Skills
- The KOH-Opalescence-Waddington Chain
What does the waddington-landscape skill do?
Waddington's epigenetic landscape: cell fate as gradient flow on potential surfaces, connecting developmental biology to dynamical systems, Schrödinger bridges, and fractional diffusion
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill waddington-landscape --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.