holomorphic-dynamics
Educational pack for holomorphic dynamics, complex iteration, fractal geometry, and data-driven dynamics (DMD/Koopman). Use this skill when the user asks about: complex dynamics, iteration on the complex plane, Julia sets, Mandelbrot sets, fixed points and stability, period doubling, bifurcation, topology of the complex plane, DMD (Dynamic Mode Decomposition), Koopman operator theory, skill dynamics as a dynamical system, fractal rendering, escape-time algorithms, or connections between dynamics and deep learning.
npx skills add majiayu000/claude-skill-registry --skill holomorphic-dynamics --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.
# Holomorphic Dynamics Educational Pack ## Overview This educational pack teaches holomorphic dynamics from first principles through ten progressive modules. Starting with iteration on the complex plane (HD-01) and building through fixed points, fractal sets, topology, and deep learning connections, the pack culminates in data-driven dynamics with Dynamic Mode Decomposition (HD-09) and Koopman operator theory (HD-10). The pack is self-contained: all complex arithmetic, iteration engines, fractal renderers, and DMD algorithms are implemented from scratch with no external math libraries. Every algorithm is transparent and educational rather than optimized for production performance. **What you will learn:** - How iteration of simple functions on the complex plane produces fractal structures of extraordinary complexity - The classification of fixed points by their multiplier and what each classification means dynamically - Why the Mandelbrot set is the "atlas" of all quadratic Julia sets - The Fatou-Julia dichotomy: stable domains versus chaotic boundaries - How period doubling cascades lead to chaos through Feigenbaum universality - The topological properties that constrain what dyna
- Overview
- Quick Start
- Module Guide
- HD-01: Iteration on the Complex Plane
- HD-02: Fixed Points and Stability
- HD-03: The Mandelbrot Set
- HD-04: Julia Sets and Fatou Sets
- HD-05: Cycles and Period Doubling
- HD-06: Topology of the Complex Plane
- HD-07: From Dynamics to Deep Learning
- HD-08: Skill-Creator as a Dynamical System
- HD-09: Dynamic Mode Decomposition
- HD-10: Koopman Operator Theory
- Core API
What does the holomorphic-dynamics skill do?
Educational pack for holomorphic dynamics, complex iteration, fractal geometry, and data-driven dynamics (DMD/Koopman). Use this skill when the user asks about: complex dynamics, iteration on the complex plane, Julia sets, Mandelbrot sets, fixed points and stability, period doubling, bifurcation, topology of the complex plane, DMD (Dynamic Mode Decomposition), Koopman operator theory, skill dynamics as a dynamical system, fractal rendering, escape-time algorithms, or connections between dynamics and deep learning.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill holomorphic-dynamics --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.